MAGNETIC RESONANCE IMAGING: PHYSICAL PRINCIPLES AND SEQUENCE DESIGN
Professor of Radiology, Electrical Engineering and Biomedical Engineering Washington University, St. Louis, MO Professor of Physics
Problem Set 3
Due: 2:00pm, Thursday, September 19th
EE 591, Fall 2013
1. Write a MATLAB function that computes the bulk magnetization vector [Mx , My , Mz ] in
the lab frame that is obtained immediate
Problem Set 8
Due: 2:00pm, Thursday, November 7th
EE 591, Fall 2013
1. You are imaging an object containing two materials, A and B. Material A has relative proton
density P DA = 1, T1 value T1,A = 100
Problem Set 6
Due: 2:00pm, Thursday, October 24th
EE 591, Fall 2013
1. For the following four acquisition schemes,
(a) Find the mathematical expression for the measured signal s(t) as a function of (x
Problem Set 11
Due: 2:00pm, Thursday, December 5th
EE 591, Fall 2013
1. Support-Limited Extrapolation using Projection onto Convex Sets (POCS).
(a) The code below generates a 1024 1024 Cartesian grid
Problem Set 6 Solutions
Due: 2:00pm, Thursday, October 24th
EE 591, Fall 2013
1. For the following four acquisition schemes,
(a) Find the mathematical expression for the measured signal s(t) as a func
Problem Set 5
Due: 2:00pm, Thursday, October 3rd
EE 591, Fall 2013
1. We wish to excite a slice described by the following picture (only the x-z plane is shown
you should assume that the picture is i
Problem Set 1
Due: 2:00pm, Thursday, September 5th
EE 591, Fall 2013
1. (Problem 2.17 from the book ) Show that:
f1 (t) ei2f0 t f2 (t) ei2f0 t = [f1 (t) f2 (t)] ei2f0 t
NOTE: In this class, we will de
Problem Set 3 Solutions
Due: 2:00pm, Thursday, September 19th
EE 591, Fall 2013
1. Write a MATLAB function that computes the bulk magnetization vector [Mx , My , Mz ] in
the lab frame that is obtained
Problem Set 8
Due: 2:00pm, Thursday, November 7th
EE 591, Fall 2013
1. You are imaging an object containing two materials, A and B. Material A has relative proton
density P DA = 1, T1 value T1,A = 100
Problem Set 9 Solutions
Due: 2:00pm, Thursday, November 14th
EE 591, Fall 2013
1. Derive the solution to the difference equation describing the spoiled low-angle gradient echo
sequence. In particular,
Problem Set 4
Due: 2:00pm, Thursday, September 26th
EE 591, Fall 2013
1. We said in class that
"
#
Mx0 y0 (0h ) cos2 (/2) Mx0 y0 (0i) sin2 (/2) Mz 0 (0 ) sin
Mx0 y0 (0 ) y0
=
.
1
Mz 0 (0 )
0 0
0
2 Mx
Problem Set 2
Due: 2:00pm, Thursday, September 12th
EE 591, Fall 2013
1. Justify that the two representations of nuclear precession shown in (A) and (B) are equivalent.
x (t) = x (0) cos(0 t) + y (0)
Final Exam: EE 591 Magnetic Resonance Imaging and Reconstruction
Due: Thursday, December 12th at 4pm
EE 591, Fall 2013
Your Name:
Directions:
There are 5 problems in the exam. Full credit requires tha
Problem Set 1 Solutions
Due: 2:00pm, Thursday, September 5th
EE 591, Fall 2013
1. (Problem 2.17 from the book ) Show that:
f1 (t) ei2f0 t f2 (t) ei2f0 t = [f1 (t) f2 (t)] ei2f0 t
NOTE: In this class,
Problem Set 10
Due: 2:00pm, Tuesday, November 26th
EE 591, Fall 2013
1. In class, we considered the FFT-based reconstruction of noisy data given by
N/21
(x) = k
X
s(nk)ei2nkx ,
n=N/2
where s(nk) is Ny
Rekil Prashanth
HomeWork#3
1)
The function is given below:
function[Mx,My,Mz]=excitation(Mx,My,Mz,w0,gamma,wrf,taup,B1)
%[Mxlab,Mylab,Mzlab]=dsolve(DMxp=delw*Myp,
DMyp=-delw*Mxp+w1*Mzp,DMzp=-w1*Myp,Mx
1
(a)
S(t) =
(x, y)ei2Gx x(t
2 )
dx dy f or < t < 2
ky
(b)
S(t) =
S(t) =
(x, y)ei2Gx x dx dy f or < t < 2
(x, y)ei2Gx x(t
1
3 )
dx dy f or 2 < t < 3
kx
ky
kx
(c)
S(t) =
(x, y)ei2Gx x(t
EE591: Magnetic Resonance Imaging and Reconstruction
Fall 2013
Instructor:
Prof. Justin P. Haldar
E-mail:
Office:
Phone:
[email protected]
EEB 442
(213)740-2358
Objectives:
Magnetic Resonance Imaging (M
(12) United States Patent
Machida
USOO6380739B1
(10) Patent N0.: US 6,380,739 B1
(45) Date of Patent: Apr. 30, 2002
(54) MULTI-ECHO SEQUENCE BASED MR
IMAGING FOR FLUID IN MOTION
(75) Inventor: Y
Phys. Med. Bioi., 1987, Vol. 32, No 10, 1345-1353. Printed in the UK
Scientijic note
A SAFE (saturate after the echo) sequence to eliminate an artefact in the measurement of T2in partially saturated
Effects on Apparent T2 in Multi Pulse Spin Echo
Bhairav B Mehta Introduction
The transverse component of the magnetization decreases gradually to zero. This is an exponential decay with the time const
Effects on Apparent T2 in Multi Pulse Spin Echo
Bhairav B Mehta Introduction
The transverse component of the magnetization decreases gradually to zero. This is an exponential decay with the time const
Investigative Radiology - Abstract: Volume 39(5) May 2004 p 288-299. and Testing of Four Multiecho Pulse Sequence Designs for Validity.
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BHAI
Novel sequence for accurate, multi-slice T2-rexometry with insensitivity to refocusing pulse profiles and reduced SAR
G. S. Pell1, A. B. Waites1, D. F. Abbott1, R. S. Briellmann1, G. D. Jackson1
1
Br
Properties of the phase-alternating phase-shift (P.[Magn Reson Imaging. 1993] - PubMed Result
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Course Announcement for Fall 2009
EE 591: Magnetic Resonance Imaging and Reconstruction
Instructor: Krishna Nayak, [email protected] EEB 406, 213-740-3494 Meeting Time: TTh 5:00-6:20pm, OHE 100C Course M