Problems and Solutions in Medical Physics

Diagnostic Imaging Physics

Kwan Hoong Ng, Jeannie Hsiu Ding Wong, Geoffrey Clarke

• Verlag: CRC Press
• Jahr: 2018
• ISBN:
  9781351006767
• Auflage: 1
• Thema: Physical Sciences
• Thema: Physics

The first in a three-volume set exploring Problems and Solutions in Medical Physics, this volume explores common questions and their solutions in Diagnostic Imaging. This invaluable study guide should be used in conjunction with other key textbooks in the field to provide additional learning opportunities. It contains key imaging modalities, exploring X-ray, mammography, and fluoroscopy, in addition to computed tomography, magnetic resonance imaging, and ultrasonography. Each chapter provides examples, notes, and references for further reading to enhance understanding.

Features:

• Consolidates concepts and assists in the understanding and applications of theoretical concepts in medical physics
• Assists lecturers and instructors in setting assignments and tests
• Suitable as a revision tool for postgraduate students sitting medical physics, oncology, and radiology sciences examinations

Basic Physics 1

1.1 TRANSMISSION INTENSITY

Problem:

Refer to the attenuation curves (Figure 1.1), explain the difference between 60 keV gamma ray and 60 kVp X-ray beam.

FIGURE 1.1 Attenuation in soft tissue for a 60 keV gamma ray and for a 60 kVp X-ray beam.

Solution:

The attenuation is the reduction in the number of photons in the beam and for photons of uniform energy (i.e. monoenergetic such as 60 keV gamma ray) it follows the simple exponential law.

$N=N_{\mathrm{o}}\text{exp}\left(-\mathrm{\mu }x\right)$

Where,

N = number of photons transmitted

N_o = initial number of photons

μ = linear attenuation coefficient (cm⁻¹)

x = thickness of material (cm)

For polyenergetic radiation, such as the 60 kVp X-ray beam, the effect of beam hardening where the lower energy photons are preferentially removed from the beam effectively reduces the slope of the curve (log intensity vs. thickness) and a pure linear relationship is no longer valid.

1.2 HVL

Problem:

If a 2 mm thick of material transmits 40% of a monoenergetic photon beam, calculate the half value layer of the beam.

Solution:

$\begin{array}{ccc}\hfill N& =\hfill & N_o\text{exp}(-\mathrm{\mu }x)\hfill \\ \hfill 0.40& =\hfill & \text{exp}(-\mathrm{\mu }(2))\hfill \\ \hfill \text{ln}(0.40)& =\hfill & -\mathrm{\mu }(2)\hfill \\ \hfill \mathrm{\mu }& =\hfill & -{\displaystyle \frac{\text{ln}(0.40)}{2}}\hfill \\ \hfill \mathrm{\mu }& =\hfill & 0.46{\text{mm}}^{-1}\hfill \end{array}$

$\text{HVL}={\displaystyle \frac{0.693}{\mathrm{\mu }}}={\displaystyle \frac{0.693}{0.46}}=1.51\text{mm}$

1.3 K-EDGE

Problem:

1. Figure 1.2 shows a mass attenuation coefficient curve. Name the peak A and suggest an element that fits this curve.
2. Explain the physics phenomenon exhibited by...