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ECSE-6963 Biological Image Analysis. Lecture #7: Common Medical Imaging Instrument: MRI & PET Scanner Badri Roysam Rensselaer Polytechnic Institute, Troy, New York 12180. Center for Sub-Surface Imaging & Sensing. Recap. Probes, media, and objects Basic types of microscopes

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ecse 6963 biological image analysis

ECSE-6963Biological Image Analysis

Lecture #7:

Common Medical Imaging Instrument:

MRI & PET Scanner

Badri Roysam

Rensselaer Polytechnic Institute, Troy, New York 12180.

Center for Sub-Surface Imaging & Sensing

  • Probes, media, and objects
  • Basic types of microscopes
  • The Radon Transform, back projection algorithm, & the X-Ray CT Scanner
magnetic resonance imaging mri
Magnetic Resonance Imaging (MRI)
  • Biggest advance since X-Rays & X-Ray CT
  • Was called “Nuclear Magnetic Resonance” in the early days
    • The word “Nuclear” made people uncomfortable during the 70’s, was not needed.
  • MRI has advanced to a point of becoming the method of choice for most parts of the body

1952 Nobel Prize: Felix Bloch and Edward Purcell

1991 Nobel Prize: Richard R. Ernst

basic principle
Basic Principle
  • Use radio waves instead of X-Rays to probe
    • Problem: Wavelength is too long!
      • Get around this limitation by producing images based on spatial variations in the phase and frequency of the radio frequency energy being absorbed and emitted by the imaged object.
  • Exploit magnetic properties of abundant particles such as protons in tissue
    • When protons are placed in a magnetic field, they become capable of receiving and then transmitting electromagnetic energy.
    • The strength of the transmitted energy is proportional to the number of protons in the tissue.
    • Signal strength is modified by properties of each proton's microenvironment, such as its mobility and the local homogeneity of the magnetic field.
    • MR signal can be "weighted" to accentuate some properties over others.
physics background spin
Physics Background - Spin
  • All physical particles (electrons, protons, neutrons….) possess a fundamental property known as spin
  • Spin is always a multiple of +/- ½ .
  • Think of spin as a tiny spinning magnet with a north pole and a south pole
  • When an external magnetic field B is applied along the z axis, the tiny magnets line up along the same axis
  • It can absorb/emit energy at a characteristic frequency
  • These frequencies are in the radio frequency range

Nuclei with highest biological abundance

behavior when a field is applied
Behavior when a field is applied
  • Each mini-magnet has two states:
    • Lined up along B, and against
    • There is an energy difference between these two states
    • Change in state involves absorbing or emitting radio-frequency energy
behavior when radio excitation is applied
Behavior when radio excitation is applied
  • At equilibrium, net magnetization vector is along B (z axis)
  • When we apply radio frequency energy at frequency , the magnetization can turn slowly away from the equilibrium angle
    • The change in angle depends on how long the RF energy is applied
    • A 90o turn can make the z component of the magnetization Mz zero (takes several milliseconds)
    • If we apply a long enough RF pulse, the magnetization can even turn by 180o
behavior when radio excitation is stopped
Behavior when radio excitation is stopped
  • If we stop this RF excitation, it returns to equilibrium

T1 = spin-lattice relaxation time

behavior when radio excitation is stopped9
Behavior when radio excitation is stopped
  • Excitation in the x-y plane makes the magnetization “precess” (wobble, like a spinning top) around the z axis.
  • Rate of precession is called the “Larmor frequency”
  • The transverse magnetization Mxy returns to equilibrium according to

T2 = spin-spin relaxation time

t 1 and t 2
T1 and T2
  • T1 is applicable along the magnetic field (axial/longitudinal)
    • Can’t be detected directly
    • Measures how quickly equilibrium is achieved with external field
  • T2 is applicable in a transverse direction to the magnetic field
    • Can be detected directly
    • Measures how long the precession persists after excitation is turned off
  • Useful to know T1 and T2 because they are characteristically different for each kind of tissue
  • These equations are for one proton
the free induction decay signal
The Free Induction Decay signal
  • A rotating magnetization will induce a current in a coil perpendicular to the z axis (say, along x axis)
  • This signal decays as T2
  • This signal is called the “free induction decay” or FID.
the 90 o fid
The 90o FID
  • The RF pulse is long enough to flip the net magnetization by 90o
  • The magnetization vector’s decay can be measured with a coil.
  • To get a strong signal:
    • Increase B0
    • Reduce temperature T
    • Material with high 
    • Material with more protons
      • In general, more spins
    • More abundant material
the overall mri signal
The Overall MRI Signal
  • There’s not enough time to establish full equilibrium in practice. If TR is the time available for recovery after the previous pulse, the longitudinal magnetization actually available is:
  •  = proton density
  • This magnetization produces the transverse magnetization in response to a 90o pulse. We measure this at time TE
weighted signals
Weighted Signals
  • By choosing TR and TE suitably, we can make one of the factors T1, T2, or  dominate
imaging process basic idea
Imaging Process: Basic Idea
  • If the external field is constant, B, then for the 3 points in the brain, the resonance frequency is the same, so they can’t be distinguished
    • We just see the sum of 3 signals
  • One way to distinguish the points is to change B, i.e., a small gradient field (about 0.01 T/m).
  • Only the points whose resonant frequency matches will respond
selecting a slice thru the patient
Selecting a Slice thru the Patient
  • Apply a linear magnetic field gradient Gzduring the time that the RF pulse is applied
  • Only the small window of z values for which the resonance frequency is matched will resonate
back projection imaging
Back-Projection Imaging
  • Apply 1-D field gradient at multiple angles in the x-y plane
  • Record MR spectra at multiple angles and use the back projection algorithm
  • Gx, Gy, and Gz are components of a 3-D field gradient
pulse sequence for back projection imaging
Pulse Sequence for Back-Projection Imaging
  • Apply a linear magnetic field gradient Gzduring the time that the RF pulse is applied to excite a slice through the patient
  • Use Gx, Gy, to set the angle while recording the signal
better technology
Better Technology


  • Use sinc-shaped pulse
  • GS selects the slice along the z axis
  • G sets the phase encoding w.r.t the y axis within the plane at the selected z value
  • Gf sets the frequency encoding w.r.t the x axis within the plane at the selected z value
image reconstruction
Image Reconstruction

Fourier Transform the FID signal to obtain a frequency spectrum for each angle

Backproject the frequency spectra to reconstruct image!

the instrument
The Instrument
  • The magnets are extremely strong (1 – 3 Tesla)
    • Enough to hurl a trashcan across a room!
  • Extremely noisy & claustrophobic inside the machine
  • Optimal design of coils, pulse sequences, and reconstruction algorithms is big business
  • Current instruments have progressed way beyond the back-projection scheme outlined here
mri images
MRI Images
  • Pixel sizes approx. 3 mm3
  • By collecting a series of images, it is possible to calculate 3 values at each pixel: T1,T2 , Proton density 
  • Different tissues show up differently on each of these “channels”
    • Basis of image segmentation!



Proton Density

mri images23
MRI Images


(trans-axial, horizontal)



ct vs mri

Cheap & Fast

Good resolution with bone

Hard to distinguish soft tissues without contrast agent

Can’t distinguish atoms beyond their X-Ray cross-section

X-Rays harmful to body


Expensive & Slow

Can distinguish bone and various soft tissues

Can distinguish specific atoms

No known health hazards to MR imaging

CT vs. MRI
main advantages of mri
Main advantages of MRI
  • Structural & Functional Imaging Possible
  • Differentiation between various kinds of soft tissue.
    • X-rays pass through soft tissue without much absorption
  • High sensitivity to early pathological changes makes early detection possible.
  • Studies of blood vessels and flow without use of contrast
    • just oxygen level of blood gives contrast
  • 3-D, allowing Multi-planar display
    • i.e. axial, sagittal, coronal, and oblique.
  • Multi-channel output
    • Enables better segmentation
  • No known biological hazards
    • Magnetic fields don’t ionize, unlike X-rays
    • Exceptions: people with pacemakers and/or implanted metallic objects can’t be imaged safely
recent developments
Recent Developments
  • Faster imaging (about 5 images/sec)
    • “Echo Planar MR” can image the brain in seconds instead of minutes
  • Of late, the importance of MRI in diagnosis is also greatly enhanced by its ability to do
    • Functional mapping of the brain
      • Exploit the fact that oxygen level differences in blood show up on MRI’s.
    • Spectroscopy and molecular imaging
nuclear medicine
Nuclear Medicine
  • Basic Idea:
    • Inject patient with radio-isotope labeled substance (tracer)
      • Chemically the same, but physically different
    • Detect the radioactive emissions (gamma rays)
      • Super-short wavelength
      • But, can’t achieve the implied high resolution
        • Detection technology limitations
        • Not enough photons!
    • Use filtered back-projection to reconstruct the 3-D image
    • Like fluorescence microscopy, except we don’t need excitation
spect pet
  • Major Functional imaging tools
    • SPECT: Single-photon Emission Computed Tomography
      • cheap and low-resolution
      • Tells us where blood is flowing
    • PET: Positron Emission Tomography
      • expensive and higher-resolution

PET image

Showing a tumor

spect instrument
SPECT Instrument
  • The “gamma camera” is a 2-D array of detectors
  • One or more gamma cameras are used to capture 2-D projections at multiple angles
  • Use filtered back-projection to reconstruct 3-D image!
    • Actual sinograms appear “noisy” due to the fact that we don’t have enough photons
    • Quantum-limited imaging

3-camera SPECT instrument

pet idea
PET Idea

Gamma Photon #1



Basic Idea:

  • Nucleus emits a positron
    • A short-lived particle
    • Same mass as electron, but opposite charge
  • Positron collides with a nearby electron and annihilates
    • Two 511 keV gamma rays are produced
    • They fly in opposite directions (to conserve momentum)



Gamma Photon #2

emission detection



Emission Detection

Ring of detectors

  • If detectors A & B receive gamma rays at the approx. same time, we have a detection
  • Hard sensor and electronics design problem, expensive
image reconstruction32
Image Reconstruction
  • We can organize our set of detections as a set of angular views
  • Use filtered back-projection algorithm!
pet images
PET Images
  • Single-channel images
  • Noisy, and blurry
    • Not ideal for segmentation
    • Segment MRI/CT for defining anatomy
    • Register the images
    • Measure activity
better algorithms
Better Algorithms
  • Filtered back-projection algorithm
    • produces a background artifact, discussed earlier
    • Noisy reconstruction
  • The Maximum Likelihood algorithm produces a better reconstruction for the same data



Maximum Likelihood

references on mri
References on MRI
  • Main MRI Reference:
  • Other MRI References
references on spect pet
References on SPECT & PET
  • PET
  • SPECT Imaging:
  • SPECT Image Atlas
  • Discussion of major medical instruments
    • Structure imaging
    • Function imaging
  • Next Class:
    • Image Pre-processing methods





& Pre-processing




& Higher-Level


assignment 2
Assignment #2

1. Create a simple 2-D phantom like the one shown in Lecture 6, and use the “radon” and “iradon” functions in MATLAB to simulate a CT scanner with 1, 2, 4, 48, and 96 angles. In other words, generate an example like the one shown in class.

Note: You should be able to do the above exercise simply by following the instructions in the tutorials on the mathworks website. They do not need specialized mathematics knowledge.

2. Search the Internet for a sample MRI image of the human brain. Plot a histogram of T1, T2 and Proton density values from this image.

3. Search the Internet for a sample PET image, and an MRI image for the same patient. Generate an overlay of the PET image over the MRI image using MATLAB or an image viewer such as PaintShop Pro or Adobe Photoshop.

instructor contact information
Instructor Contact Information

Badri Roysam

Professor of Electrical, Computer, & Systems Engineering

Office: JEC 6046

Rensselaer Polytechnic Institute

110, 8th Street, Troy, New York 12180

Phone: (518) 276-8067

Fax: (518) 276-6261/2433



NetMeeting ID (for off-campus students):

Secretary: Jeanne Denue, JEC 6049, (518) 276 –6313,