Medical physics

What medical physics covers

One of the five AQA option units, so confirm it is the one you sit. It has two halves: the eye and the ear treated as physical instruments, together with the electrical signal of the heart, and then three ways of imaging the inside of a body, by echo, by shadow and by tracer. Lenses, exponential attenuation, half-life and annihilation all reappear here.

The main ideas

• The eye as a converging system with a fixed image distance, accommodation as a change of power, the two defects corrected, astigmatism, and rods and cones.
• Sound through the outer, middle and inner ear, why the middle ear raises the pressure, intensity and the decibel scale, and equal loudness curves.
• The electrocardiogram: where the pd comes from, what the amplifier must do, and the P wave, QRS complex and T wave.
• Ultrasound: the piezoelectric transducer, pulse-echo timing, acoustic impedance and the reflection coefficient, the coupling gel, and A against B scans.
• X-rays: the tube, the continuous and characteristic spectra, attenuation and half-value thickness, contrast media, detectors, and how CT builds a cross-section.
• Radionuclide imaging: choosing a tracer's half-life and emission, the three half-lives, the gamma camera, and PET with coincidence detection of two 511 keV photons.

The equations it turns on

P = 1f      1u + 1v = 1f$P = \frac{1}{f} \qquad \frac{1}{u} + \frac{1}{v} = \frac{1}{f}$P = (1/f) (1/u) + 1/v = 1/f

lens power, and the eye or a correcting lens

intensity level in dB = 10 logII₀$\text{intensity level in dB} = 10\,\text{log}\frac{I}{I_0}$intensity level in dB = 10 log (I/I_0)

loudness, used in both directions

Z = ρc      reflected fraction = (Z₂ - Z₁)²(Z₂ + Z₁)²$Z = \rho c \qquad \text{reflected fraction} = \frac{(Z_2 - Z_1)^2}{(Z_2 + Z_1)^2}$Z = ρc reflected fraction = ((Z_2 - Z_1)^2)/((Z_2 + Z_1)^2)

acoustic impedance, and what reflects at a boundary

d = ct2$d = \frac{ct}{2}$d = ct/2

depth of a boundary from a pulse-echo time

I = I₀e^-μx$I = I_{0}e^{-\mu x}$I = I_0e^(-μx)

attenuation of a beam through a thickness of tissue

1T_E = 1T_P + 1T_B$\frac{1}{T_E} = \frac{1}{T_P} + \frac{1}{T_B}$1/T_E = 1/T_P + 1/T_B

effective half-life from physical and biological

Where it usually goes wrong

• The decibel scale is logarithmic, so ten more decibels is ten times the intensity, and intensities cannot be combined by adding decibel values.
• A large impedance mismatch reflects almost the whole pulse, which is why air between probe and skin is excluded with gel. Imaging depends on small mismatches, which give faint echoes at every boundary and let the pulse travel deeper.
• Correcting lens calculations start from what the lens must do: for myopia, take an object at infinity to the far point; for hypermetropia, the normal near point to the actual one.
• In radionuclide imaging and PET the radiation comes from inside the patient, which makes the choice of half-life and emission a safety question as well as an imaging one.

Where to start

The eye, the ear and biological measurement are self-contained and can be revised in any order. In the imaging half take ultrasound, then X-rays and CT, then radionuclide imaging and PET, which assumes annihilation from Particles and half-life from Nuclear physics.