UCL DEPARTMENT OF MEDICAL PHYSICS AND
BIOMEDICAL ENGINEERING






Assessed Coursework

Module Code: MPHY0019
Module Title : MRI and Biomedical Optics
Coursework Title : Biomedical Optics Coursework (Level 7 students only)
Lecturer: Dr. Rob Cooper
Date Released: Thursday 27th January 2022


Please submit via Moodle before midnight on the day of the deadline:

Coursework Deadline: Wednesday 16th February 2022


Before completing and submitting this piece of coursework please check that you are fully aware
of the MPBE policy on plagiarism (See your Student Handbook).


MAKE SURE TO ATTACH A COMPLETED COVER SHEET TO YOUR COURSEWORK
BEFORE SUBMISSION. DO NOT INCLUDE YOUR NAME IN YOUR COURSEWORK.





Biomedical Optics: Coursework 2022:


Question 1.


A sample of tissue consists of a layer of skin of thickness over a layer of muscle of thickness . A
laser beam is directed at the tissue and provides a fluence rate of = $ at the surface
of the skin. At the wavelength of the beam, the absorption coefficient of the skin layer is =. $, and the absorption coefficient of the muscle layer is = . $.

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 = . $.

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.
[2]

Given now that = . and = :

c) Calculate the fluence rate of the light exiting the sample at the point marked ‘x’.
[3]

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 = . , and given the photon diffusion equation:



where is the fluence rate, represents an internal optical source, and is the optical diffusion
coefficient:

e) Calculate a more accurate answer to part (c). Justify any assumptions you make.
[5]

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
(3) of each chromophore at each wavelength, are given in the table below.

690 nm 740 nm 850 nm
Measured power (mW) 7.87 7.90 7.92 " (cm-1M-1) 956 1275 2526 " (cm-1M-1) 4933 3058 1797 " (cm-1M-1) 11200 10020 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.
[3]

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 M and
beware of rounding errors.
[3]


*This site lets you do matrix inversions (https://matrix.reshish.com/inverse.php) and multiplications
(https://matrix.reshish.com/multiplication.php). Click the ‘Insert Matrix’ button to paste values to minimize errors.
1
c
∂Φ
∂t = −µaΦ+∇⋅ κ∇Φ( )+ q0