Ultrasound: Seeing Inside the Body Without Surgery!
Hello future Physicists! Welcome to one of the most practical and fascinating chapters in A Level Physics: the world of ultrasound. Don't worry if 'Medical Physics' sounds intimidating—we are simply applying the wave concepts you already know (like reflection and intensity) to amazing real-world technology.
In this section, you will learn how high-frequency sound waves are made, how they interact with tissues, and how we use those echoes to create detailed diagnostic images, such as those famous baby scans!
1. What is Ultrasound? (A Quick Review)
Before diving into the complex devices, let's quickly define our wave.
Sound Waves are longitudinal waves—they require a medium (like air or tissue) to travel through. We humans can typically hear frequencies between 20 Hz and 20 kHz.
Ultrasound is defined as sound waves with a frequency greater than 20 kHz (or 20,000 Hz). In medical applications, frequencies are typically in the MHz range (1 to 20 MHz).
Key Takeaway
Ultrasound is simply sound too high-pitched for humans to hear, used primarily in medicine because higher frequencies allow for better resolution (detail) in imaging.
2. Producing and Detecting Ultrasound: The Piezo-Electric Transducer
2.1 The Piezo-Electric Effect
The magic of ultrasound generation and detection lies in a special component called the piezo-electric crystal (often made of materials like quartz or specific ceramics).
The piezo-electric effect works two ways:
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Generating Ultrasound (The Speaker Function):
When an alternating Potential Difference (p.d.) is applied across the crystal, it causes the crystal to physically compress and expand (change its shape). This rapid mechanical oscillation (vibration) produces ultrasound waves. The frequency of the applied p.d. determines the frequency of the emitted ultrasound.
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Detecting Ultrasound (The Microphone Function):
When an incoming ultrasound wave hits the crystal, the mechanical force causes the crystal's shape to change (deform). This change in shape generates a transient e.m.f. (voltage) across the crystal. This voltage signal is then used by the processing unit to build the image.
Analogy: Think of the piezo crystal as a tiny drum skin that can both be hit to make a sound, and detect tiny movements to hear a sound.
The device containing this crystal, used for both transmission and reception, is called a piezo-electric transducer (or probe).
Quick Review: Piezo-Electric Effect
- P.D. applied $\rightarrow$ Crystal changes shape $\rightarrow$ Ultrasound Generated (Production).
- Ultrasound hits $\rightarrow$ Crystal changes shape $\rightarrow$ E.M.F. Generated (Detection).
3. Using Ultrasound for Diagnostics: Reflection
3.1 The Imaging Process
To image internal structures, the transducer sends out a short, high-frequency pulse of ultrasound. This pulse travels through the body until it hits a boundary (interface) between two different types of tissue (e.g., muscle meeting bone, or fluid meeting muscle).
At this boundary, some of the sound energy is transmitted forward, and some is reflected back as an echo to the transducer.
By measuring two things, we get diagnostic information (LO 3):
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Time Delay: The time taken for the echo to return tells us the depth of the boundary.
(Since sound travels at speed \(c\), the distance to the boundary \(x\) is half the total path length: \(x = (c \times t) / 2\)) - Reflected Intensity: The strength of the returning echo tells us about the nature of the boundary (how different the two media are).
3.2 Specific Acoustic Impedance (\(Z\))
The key factor determining how much sound reflects at a boundary is a property of the material called the Specific Acoustic Impedance, \(Z\).
Think of \(Z\) as the material's 'resistance' to the passage of sound.
Definition: The specific acoustic impedance \(Z\) is defined as the product of the density of the medium, \(\rho\), and the speed of sound in the medium, \(c\).
Formula: $$Z = \rho c$$
Where:
- \(\rho\) is the density (kg m\(^{-3}\)).
- \(c\) is the speed of sound (m s\(^{-1}\)).
- The unit of \(Z\) is kg m\(^{-2}\) s\(^{-1}\).
3.3 Intensity Reflection Coefficient (\(R\))
When ultrasound hits a boundary between medium 1 (impedance \(Z_1\)) and medium 2 (impedance \(Z_2\)), the fraction of the incident intensity that is reflected is given by the intensity reflection coefficient, \(R\).
Formula: (LO 5) $$R = \frac{I_R}{I_0} = \left(\frac{Z_1 - Z_2}{Z_1 + Z_2}\right)^2$$
Where:
- \(I_R\) is the reflected intensity.
- \(I_0\) is the incident intensity (the intensity hitting the boundary).
Understanding the Reflection:
This formula is extremely important in medical imaging. The size of the reflected signal depends on the difference between the two impedances, \(Z_1 - Z_2\):
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Maximum Reflection (Large Difference): If there is a very large difference in \(Z\) (e.g., sound traveling from tissue to air, or tissue to bone), the magnitude of \((Z_1 - Z_2)\) is large. \(R\) approaches 1 (or 100% reflection).
This is why air must be removed using gel when performing an ultrasound scan—a tissue-air boundary reflects almost all the sound, blocking visibility deeper inside the body.
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Minimum Reflection (Small Difference): If the two impedances are very similar (matched), then \(Z_1 \approx Z_2\). This makes the numerator \((Z_1 - Z_2)\) close to zero. \(R\) approaches 0 (nearly all sound is transmitted).
For good deep tissue imaging, we need low reflection so that the sound can penetrate far into the body.
Key Takeaway
The quality of an ultrasound image relies on the fact that different soft tissues (like muscle, fat, and fluid) have slightly different acoustic impedances, causing small, measurable reflections (echoes) that allow us to map the structure.
4. Attenuation of Ultrasound
4.1 What is Attenuation?
As the ultrasound wave travels through the body, its intensity gradually decreases. This loss of intensity (or energy) is called attenuation.
Attenuation occurs because:
- The wave spreads out (divergence).
- Energy is absorbed by the tissue (converted into heat).
- Energy is reflected or scattered at boundaries.
4.2 The Attenuation Formula
The decrease in intensity is an exponential process, meaning it decays faster at the start than later on (LO 6).
Formula: $$I = I_0 e^{-\mu x}$$
Where:
- \(I\) is the intensity after travelling a distance \(x\).
- \(I_0\) is the initial intensity.
- \(x\) is the distance travelled in the medium (m).
- \(\mu\) is the attenuation coefficient (m\(^{-1}\)).
The Role of the Attenuation Coefficient (\(\mu\))
The value of \(\mu\) is crucial. It dictates how quickly the intensity drops in a given medium.
- Higher \(\mu\) means faster intensity loss (more attenuation).
- \(\mu\) increases with frequency: Higher frequency ultrasound gives better image resolution but is attenuated more strongly. This is a crucial trade-off.
Example: A high-frequency (10 MHz) scan gives a brilliant picture of a shallow structure (like the eye), but a low-frequency (3 MHz) scan is needed to penetrate deep into the abdomen, even though the image is less detailed.
Common Pitfall Alert!
Don't confuse the two formulas!
- Reflection Formula \((I_R/I_0)\) tells you how much intensity is lost at a boundary (a single point).
- Attenuation Formula \((I = I_0 e^{-\mu x})\) tells you how much intensity is lost while travelling through a continuous medium (over a distance \(x\)).
Chapter Summary: Production and Use of Ultrasound
Harnessing the Wave
Ultrasound is an amazing application of wave physics, allowing us to safely look inside the human body. The process is entirely dependent on the two-way function of the piezo-electric transducer (converting electrical energy to sound and back again) and the physics of wave interaction at tissue boundaries.
Essential Formulas to Remember
1. Specific Acoustic Impedance:
$$Z = \rho c$$2. Intensity Reflection Coefficient:
$$\frac{I_R}{I_0} = \left(\frac{Z_1 - Z_2}{Z_1 + Z_2}\right)^2$$3. Attenuation (Decay of Intensity):
$$I = I_0 e^{-\mu x}$$