MRI Simulation Coursework 2019: Task I and II Analysis

This document presents a comprehensive MRI simulation coursework, encompassing detailed analysis of magnetic resonance imaging principles. The coursework, completed using Matlab, explores key concepts such as T1 and T2 relaxation times, spin echo and inversion recovery sequences, and their impact on signal contrast within different brain tissues including white matter, grey matter, and cerebral spinal fluid. The student analyzes the effects of varying parameters like TR, TE, and flip angles on image contrast, determining optimal settings for specific imaging scenarios. Furthermore, the coursework delves into the contrast mechanisms of the inversion recovery technique, demonstrating its utility in differentiating between tissues and potentially identifying disruptions in the blood-brain barrier. The document includes Matlab code snippets and figures illustrating the contrast behavior, alongside the student's findings and interpretations of the simulation results.

MRI Coursework 2019
Student details

TASK I
The MRI is the application of the NMR to determine the brain imaging. The signal in voxel
depends on proton density, the T1 relaxation, and the T2 relaxation. There are three tissues being
analyzed namely cerebral spinal fluid, white matter, and grey matter.
The spin echo removes the effect of static magnetic fields using a 180 degree RF pulse. The
sequence to image the brain with the signal,
I ∝ M 0 ( 1−e
−TR
T 1 ) , e
−TE
T 2
S ( Te ,Tr ) =S0 e
(−T E
T2 ) (1−e
−T R
T 1 )
PART A
The TR length needed to minimize the T1 effects on WM/GM signal.
. e− Te
T2
¿
2 2 ms
PART B
Magnetism with echo time assuming a negligible influence of T1 for WM and GM using the
maximum; to determine the magnetism,
M xy =M0
1−e
Tr
T1
1−cos α . e
−Tr
T1
sin α . e− T e
T2
¿
1 | P a g e

For the spin echo images,
SSE =ρ . [1−e
−T R
T1 ] . e
−
( TE
T 2 )
2 | P a g e

PART C
Providing a contrast such that, from the following equation,
SSE =ρ . [1−e
−T R
T1 ] . e
−
( TE
T 2 )
T 1 factor= [ 1−e
−T R
T 1 ]
T 2 factor=e− ( TE
T2 )
The contrast is given by,
C=
| S A −SB
SA + SB |
Swm=S0.*exp((-Twme/Twm2)*(1-exp(-Twmr/Twm1)));
Sgm=S0.*exp((-Tgme/Tgm2)*(1-exp(-Tgmr/Tgm1)));
S=abs((Sgm-Swm)/(Sgm+Swm)); %Demonstrates the contrast
figure(1)
plot(Twmr,Swm,'r-.')
hold on
plot(Tgmr,Sgm,'b-.')
grid on
hold off
title('Part B')
For T1 dependency,
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For T2 dependency,
PART D
The optimal TE based on C is 92ms.
PART E
Increasing the relaxation time, T1, weighting implies a decrease in Tr. The same happens for the
T2 dependency as well. It is observed from the contrast that the relaxation time, T1, takes longer
to minimize compared to T2. Using different angles, yields different contrast values.
PART F
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The white matter tissue appears brighter. The relaxation time T2, the contrast affects the
brightness of the white matter as illustrated in the figures below,
TASK II
Mz (t )=M 0 (1−2 e
−t
T 1 )
Part A
Plotting the T1 recovery curve based on the inversion pulse for CSF considering that the M0 lies
on the z-plane following the pulse,
5 | P a g e

Part B
To perform the inversion recovery images, the following equation is used,
SIR= ρ. [ 1−2 e
−T1
T 1
+e
−T R
T 1 ] . e
−T E
T2
Part C
The magnetism preparation affects the contrast between the GM and WM used in the task I with
the echo time incorporating the signal inversion to null CSF such that,
WM and GM contrast dependency on T1, TR, and TE is demonstrated based on the IR gold
standard technique for T1 contrast.
function [Afp,Bfp]=freeprecess(T,T1,T2,df)
%
% Function simulates free precession and decay
% over a time interval T, given relaxation times T1 and T2
% and off-resonance df. Times in ms, off-resonance in Hz.
phi = 2*pi*df*T/1000; % Resonant precession, radians.
E1 = exp(-T/T1);
6 | P a g e
. e− Te
T2
¿
. e− Te
T2
¿

E2 = exp(-T/T2);
Afp = [E2 0 0;0 E2 0;0 0 E1]*zrot(phi);
Bfp = [0 0 1-E1]';
Part D
The contrast between GM and WM has been altered such that, the signal increases at SE imaging
by a factor of 2-4. One can detect the disruption of the blood brain barrier which would imply a
tumor grading.
7 | P a g e

APPENDIX
%% MRI simulation coursework
... Student name
... Student Reg Number
%% Task 1
clear all
close all
clc
% Part B
Twme=8.9;
Twmr=0:0.5:100;
Twm1=560; %ms
Twm2=82; %ms
S0=1.5;
%for the grey matter in the brain images
Tgme=87;
Tgmr=0:0.5:100;
T=0:0.5:100; %contrast
Tgm1=1100; %ms
Tgm2=92; %ms
%for the cerebral part
Tcsf1=2000; %ms
Tcsf2=200; %ms
Swm=S0.*exp((-Twme/Twm2)*(1-exp(-Twmr/Twm1)));
Sgm=S0.*exp((-Tgme/Tgm2)*(1-exp(-Tgmr/Tgm1)));
S=abs((Sgm-Swm)/(Sgm+Swm)); %Demonstrates the contrast
figure(1)
plot(Twmr,Swm,'r-.')
hold on
plot(Tgmr,Sgm,'b-.')
grid on
hold off
title('Part B')
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