MAGNETIC RESONANCE IMAGING: PHYSICAL PRINCIPLES AND SEQUENCE DESIGN
Professor of Radiology, Electrical Engineering and Biomedical Engineering Washington University, St. Louis, MO Professor of Physics Case Western Reserve University, Cleveland, OH
E
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 immediately after applying a rectangular RF pulse to a spin
syst
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 = 1000 ms, and T2 value T2,A = 50 ms. Material B has
relativ
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, y).
Assume an isochromatic spin system.
(b) Assuming
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 of k-space samples using the
analytic Shepp-Logan phant
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 function of (x, y).
Assume an isochromatic spin system.
(b)
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 identical for each value of y):
z
3.5 mm
3 mm
x
6 mm
(a)
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 define the convolution of continuous signals as:
Z
g (x
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 immediately after applying a rectangular RF pulse to a
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 = 1000 ms, and T2 value T2,A = 50 ms. Material B has
relativ
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, let Mz [n] denote the z-magnetization immediately befo
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 y (0 ) + Mx0 y 0 (0 ) sin + Mz (0 ) cos
(a) Prove thi
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) sin(0 t)
y (t) = x (0) sin(0 t) + y (0) cos(0 t)
(A)
z
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 that you show work and justify all
answers. Please read al
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, we will define the convolution of continuous signals as
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 Nyquist-sampled noisy data that can be decomposed as
s(nk
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,Mxp(0)=Mx,
Myp(0)=My,Mzp(0)=Mz,t)
%Using the above equati
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
2 )+Gpe y( )
dx dy f or < t < 3
ky
Gpe
kx
2
(d)
S(t
EE591: Magnetic Resonance Imaging and Reconstruction
Fall 2013
Instructor:
Prof. Justin P. Haldar
E-mail:
Office:
Phone:
jhaldar@usc.edu
EEB 442
(213)740-2358
Objectives:
Magnetic Resonance Imaging (MRI) technology has developed into
a powerful tool for i
(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: Y0shi0 Machida, Nasu-Gun (JP)
(73) Assignee: Kabushiki
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 NMR systems
Paul S Tofts and G Johnson
Institute
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 constant as T 2. T2 relaxation time is time constant fo
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 constant as T 2. T2 relaxation time is time constant fo
Investigative Radiology - Abstract: Volume 39(5) May 2004 p 288-299. and Testing of Four Multiecho Pulse Sequence Designs for Validity.
LWWOnline | LOGOUT | eALERTS | PROFILE | CUSTOMER SUPPORT
BHAIRAV MEHTA [INSTITUTION]
Home
Search
Current Iss
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
Brain Research Institute, Heidelberg West, Victoria,
Properties of the phase-alternating phase-shift (P.[Magn Reson Imaging. 1993] - PubMed Result
My NCBI [Sign In] [Register]
NCBI
PubMed
A service of the U.S. National Library of Medicine and the National Institutes of Health
All Databases PubMed