Radiation Physics: Interaction of X-rays and Gamma Rays with Matter

Introduction

In this chapter, we will delve into the mechanisms through which x-rays and gamma rays interact with matter. Understanding these interactions is crucial for medical imaging, as they form the basis of image creation and influence the quality of the images obtained.

Electromagnetic Spectrum Context

X-rays and gamma rays are part of the electromagnetic spectrum, positioned next to each other due to their similar wavelengths and energy ranges. The wavelengths range from 1 nanometer to 1.1 picometers, and their energy ranges from 1 keV to 10 MeV.

Interaction Mechanisms

The primary interactions of x-rays and gamma rays with matter are:

1. Transmission

2. Absorption

3. Scattering

These interactions can be analogized to shining a torch through a translucent plastic sheet.

Transmission

When x-rays pass through a medium without interacting, they are transmitted. In the context of medical imaging, these transmitted rays contribute to the formation of the image by reaching the x-ray detector.

Absorption

Absorption occurs when x-rays are absorbed by the medium, converting their energy into other forms such as heat. This is critical for image formation as different tissues absorb x-rays to varying degrees, creating contrast in the image.

Scattering

Scattering happens when x-rays are deflected from their original path. Scatter radiation can degrade image quality by causing fogging on the x-ray film, thus reducing image contrast.

X-ray Interaction with the Human Body

When x-rays encounter the human body, three main interactions determine the image formation:

1. Bone Absorption

2. Soft Tissue Transmission

3. Scattering by Various Tissues

Bone Absorption: Bones, being dense, absorb most of the x-rays, appearing white on the x-ray film because the x-rays are blocked and do not reach the detector.

Soft Tissue Transmission: Soft tissues allow more x-rays to pass through compared to bones, leading to varying shades of gray on the x-ray film.

Scattering: Scattered x-rays can contribute to image noise, reducing the sharpness and clarity of the image.

Example of Image Formation

Consider a torch shining through a translucent plastic sheet. A significant portion of light is transmitted, some light is absorbed, and some is scattered. Similarly, in x-ray imaging, bones absorb most of the x-rays, while soft tissues allow more x-rays to pass through, and some x-rays are scattered, contributing to the image's overall quality.

Attenuation

Attenuation is the reduction in the intensity of the x-ray beam as it passes through matter. It is described by the following key concepts:

1. Half-Value Layer (HVL)

2. Linear Attenuation Coefficient (µ)

3. Mass Attenuation Coefficient (µ/ρ)

Half-Value Layer (HVL): HVL is the thickness of a material required to reduce the intensity of the x-ray beam by half. It is inversely proportional to the material's ability to block x-rays.

HVL = 0.693/μ

Linear Attenuation Coefficient (µ): µ is a measure of how easily a material can attenuate the x-ray beam. It depends on the material's density and atomic number.

μ = 0.693/HVL

Mass Attenuation Coefficient (µ/ρ): This coefficient normalizes the linear attenuation coefficient by the material's density, making it independent of density variations.

μ/ρ = LAC ÷ density

Intensity and Attenuation Formula

The intensity of the x-ray beam after passing through a material can be described by the exponential attenuation formula:

I = I₀ e^(-μx)

Where:

• I is the transmitted intensity.

• I₀​ is the initial intensity.

• μ is the linear attenuation coefficient.

• x is the thickness of the material.

This formula highlights how the intensity of the x-ray beam decreases exponentially with the thickness of the absorbing material.

Example Analogies for Better Understanding

1. Torch and Plastic Sheet: Imagine shining a torch through a translucent plastic sheet. Some light passes through (transmission), some is absorbed by the sheet (absorption), and some is scattered in different directions (scattering). This analogy helps in understanding how x-rays interact with different tissues in the body.

2. Floodlight and Translucent Object: Using a floodlight instead of a torch shows that a more intense light source can reduce the sharpness of the shadow formed, similar to how higher x-ray energy can reduce image contrast.

Conclusion

Understanding the interactions of x-rays and gamma rays with matter is fundamental for interpreting medical images. These interactions—transmission, absorption, and scattering—determine the contrast and quality of the images, which are crucial for accurate diagnosis and treatment planning.

This chapter provides a comprehensive overview of the principles governing x-ray interactions with matter, incorporating both theoretical concepts and practical analogies to facilitate understanding. Further sections will delve into specific effects such as the Compton effect and photoelectric effect, which play significant roles in medical imaging.