UCL DEPARTMENT OF MEDICAL PHYSICS AND BIOMEDICAL ENGINEERING
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MRI and Biomedical Optics
Biomedical Optics Coursework (Level 7 students only) Dr.
Thursday 27th January 2022
Please submit via Moodle before midnight on the day of the deadline: Coursework Deadline: Wednesday 16th February 2022
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Biomedical Optics: Coursework 2022:
Question 1.
A sample of tissue consists of a layer of skin of thickness 𝒅𝟏 over a layer of muscle of thickness 𝒅𝟐. A laser beam is directed at the tissue and provides a fluence rate of 𝚽𝟎 = 𝟓𝟎 𝒎𝑾𝒄𝒎$𝟐 at the surface of the skin. At the wavelength of the beam, the absorption coefficient of the skin layer is 𝝁𝒂𝟏 = 𝟎. 𝟎𝟓 𝒎𝒎$𝟏, and the absorption coefficient of the muscle layer is 𝝁𝒂𝟐 = 𝟎. 𝟎𝟏 𝒎𝒎$𝟏.
a) Assuming scattering can be ignored, draw a plot of the fluence rate of the laser beam against distance into the sample (z). Include as much detail as you can.
[2] A better model of this tissue sample accounts for the optical scattering of the muscle layer, with
scattering coefficient 𝝁𝒔𝟐 = 𝟓. 𝟏 𝒎𝒎$𝟏.
b) Draw a plot of the fluence rate of the collimated laser beam against distance into the sample for
this improved model. Include as much detail as you can.
Givennowthat𝒅𝟏 =𝟎.𝟒𝒎𝒎and𝒅𝟐 =𝟏𝟎𝒎𝒎:
c) Calculate the fluence rate of the light exiting the sample at the point marked ‘x’.
d) What assumptions are implicit to your calculation in part (c) – why might the answer be inaccurate? [2]
Given that for muscle, the anisotropy factor 𝒈 = 𝟎. 𝟖, and given the photon diffusion equation: 1 ∂Φ = −μ Φ + ∇ ⋅ κ∇Φ + q
where 𝚽 is the fluence rate, 𝒒𝟎 represents an internal optical source, and 𝜿 is the optical diffusion
coefficient:
e) Calculate a more accurate answer to part (c). Justify any assumptions you make.
The skin layer of the sample is separated from the muscle and examined using a spectroscopic measurement. This measurement uses three optical sources, with wavelengths 690 nm, 740 nm and 850 nm to determine the concentration of the chromophores oxyhaemoglobin, deoxyhaemoglobin and melanin in the skin. Each source provides 8 mW of optical power, and the powers transmitted through the skin layer are measured. The results of this measurement, and the specific absorption coefficients (𝜶3) of each chromophore at each wavelength, are given in the table below.
Measured power (mW) 𝜶”𝑶𝒙𝒚𝒉𝒂𝒆𝒎𝒐𝒈𝒍𝒐𝒃𝒊𝒏 (cm-1M-1)
𝜶”𝑫𝒆𝒐𝒙𝒚𝒉𝒂𝒆𝒎𝒐𝒈𝒍𝒐𝒃𝒊𝒏 (cm-1M-1) 𝜶”𝑴𝒆𝒍𝒂𝒏𝒊𝒏 (cm-1M-1)
7.87 956 4933 11200
7.90 1275 3058 10020
7.92 2526 1797 8860
f) Write out a matrix equation that relates the concentration of each chromophore to the optical
powers measured at each wavelength. Define any symbols you use.
g) Using Matlab, or an online matrix calculator*, or any other approach, determine the concentrations of oxyhaemoglobin, deoxyhaemoglobin and melanin in this sample. Give your answers in 𝜇M and
beware of rounding errors.
[3] (https://matrix.reshish.com/multiplication.php). Click the ‘Insert Matrix’ button to paste values to minimize errors.
*This site lets you do matrix inversions (https://matrix.reshish.com/inverse.php) and multiplications
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