Quantitative magnetic resonance imaging (Q-MRI) differs sharply from conventional directly acquired MRI in that objective measures (such as the trio of basic MR properties: T1, T2, and proton density[PD]) are used for analysis as well as further postprocessing rather than relative signal intensities. This paper will recount a brief history of the origins and applications of Q-MRI for measurement of T1 and T2 relaxation times and PD, as well as discuss the basic theoretical underpinnings. A variety of postprocessing options as well as a review of the scientific literature regarding clinical applications of these techniques over the past 30 years are addressed.
is currently a fourth-year Radiology Resident at Boston
University Medical Center, Boston, MA. He earned his BA in
Biology from the University of Pennsylvania, his BS in Health
Care Management from the Wharton Undergraduate School of
Business, and his MD from the University of Pennsylvania School
of Medicine, Philadelphia, PA. He completed a transitional-year
Internship at Advocate Ravenswood Medical Center, Chicago, IL,
before entering residency. Dr. Chang will begin a Cross-Sectional
Imaging Fellowship at Johns Hopkins Hospital, Baltimore, MD in
is an Associate Professor of Radiology and an Adjunct Associate
Professor in the School of Biomedical Engineering at the Boston
University School of Medicine, Boston, MA.
Most radiologic interpretation with magnetic resonance (MR)
imaging has focused on qualitative visual assessment of anatomy and
disease processes rather than quantitative analysis. This method of
interpretation has served to define gross extent of disease when
anatomic changes manifest as visibly detectable differences in
signal intensity. If scan parameters and timings are not set
optimally prior to scanning or if the patient is unable to
cooperate throughout the entire length of a study, qualitative
interpretation of the resulting directly acquired images suffers
dramatically. In these ways, the current conventional practice of
MR imaging may be seen as relatively inefficient in the extraction
of MR information from tissues and organs when compared with
quantitative MR imaging (Q-MRI) techniques.
Conventional or directly acquired MR images are qualitative and
contrast-weighted where pixel values have meaning only in relation
to other pixel values. These pixel values are dependent on a
complex mix of proton density (PD), longitudinal relaxation time
(T1), and transverse relaxation time (T2) based on the initial scan
settings. Q-MRI portrays the spatial distribution of absolute
biophysical parameter measurements on a pixel-by-pixel basis.
Biophysical parameters quantified by Q-MRI include the primary
triad of T1, T2, and PD. Other parameters currently measured in
clinical practice are the diffusion coefficient and diffusion
tensor, perfusion, and blood-oxygen-level dependence (BOLD) in
functional MR imaging. Quantitative parameters investigated
experimentally have also included T2*, T1ρ, and the magnetization
transfer ratio. These quantitative measures are theoretically
independent of experimental settings (such as magnetic and
radio-frequency [RF] field, inhomogeneity, receiver gain, and coil
sensitivity), and are thus absolute and comparable between
different scanners, different institutions, and over differing
points in time.
Quantitative and qualitative MR imaging offer complementary
medical information and use the same technology platform and
equipment. While the patient information generated with
conventional scanning is primarily visual, Q-MRI portrays
information that is intrinsically more tissue-spe-cific and is
consequently less dependent on subjective visual assessment. The
quantitative data generated by Q-MRI (eg, T1, T2, and PD maps) can
also be postprocessed to take advantage of new ways of looking at
the wealth of in-formation available such as segmentation based on
biophysical properties and anat-omy, distribution histograms, and
synthetic MR images of user-definable and variable weighting
(variable at the time of image interpretation).
The purpose of this paper is to delineate the principles of
Q-MRI relaxometry and to provide a review of its clinical
Quantitative MR imaging principles
The defining aspect of quantitative image information, as
opposed to qualitative image information, is that quantitative
pixel values are devoid of extraneous experimental information and
are therefore largely tissue-specific. Accordingly, Q-MRI may be
viewed as a collection of MR imaging techniques with which the
tissue-specific information contained in the directly acquired
images can be separated from experimental conditions.
Generating quantitative MR images of the human body is
accomplished in 2 phases. First, a Q-MRI pulse sequence is employed
to generate directly acquired images. For every slice, there are 2
or more images that are identical in all experimental conditions
except for the weighting in the target parameter (eg, T1, T2, etc).
In the second phase, these differentially weighted images are
processed with a Q-MRI algorithm used for computing maps of the
target parameter. The focus of this article is Q-MRI applications
of proton density and the 2 primary relaxation times (T1 and T2);
however, most of these principles and techniques apply to many
other parameters such as diffusion, flow, magnetization transfer,
and so forth. Although the principle of quantitative MRI by
differential weighting applies to many tissue parameters, the pulse
sequences and quantitative MRI post-processing algorithms are, in
general, very different from tissue parameter to tissue
Origins of quantitative MR imaging
Using nuclear MR (NMR) relaxometry to detect disease predates
the advent of MR imaging. Damadian
first reported alteration of T1 relaxation times in cancerous
tumors in 1971. In the early 1980s, vast amounts of experimental
quantitative NMR measurements of biological tissues (animal and
human, normal and diseased) were published and reviewed by
Bottomley and colleagues.
Crooks and coworkers
also speculated on the value of relaxation times in MR imaging.
Extrapolating to MR imaging this
"NMR-relaxometry-disease-signature" concept was logical and
intellectually appealing. Indeed, many seminal papers on Q-MRI
pulse sequence design and theory were published in the early 1983
to 1988 period, only a few years after the advent of clinical MR
Whereas quantitative NMR relaxometry applies to tissues on a
whole-specimen basis, quantitative MR imaging is analogous to
performing many quantitative NMR measurements in parallel on the
much smaller voxel size scale.
T1 quantitative MR imaging
T1 is a measure of the promptness of a tissue to return to its
longitudinal state of magnetic equilibrium, M
, after removal from equilibrium with an RF pulse. This
equilibration phenomenon is caused by interactions with the tissue
lattice; hence, T1 is known as the spin-lattice relaxation time.
The equilibration of the longitudinal magnetization is an
exponential recovery process; for example, after application of a
180º inversion pulse in the setting of very long repetition times
(TR), the longitudinal magnetization recovery as a function of time
(Figure 1) can be approximated by the equation:
(See Equation 1.)
This equation can be rearranged with basic algebraic
manipulations to give the following:
(See Equation 2.)
Hence, if the logarithmic quantity in the left-hand side is
plotted as function of time, a straight line is predicted.
Furthermore, the slope of this line is equal to the inverse of T1.
This is the basis of Q-MRI algorithms for estimating T1 with
multi-inversion time (TI) experiments. Theoretically, a minimum of
only 2 points (ie, 2 inversion times) is required to determine the
slope of this line, and, hence T1, though more measured points
result in a more accurate slope estimation with noisy data. A
comprehensive discussion of T1 calculations can be found in a
recent review by Kingsley.
T2 quantitative MR imaging
T2 is a measure of the promptness of a tissue to return to its
null transverse state of magnetic equilibrium, after removal from
equilibrium with a radiofrequency excitation pulse. This
equilibration phenomenon is caused by interactions with other
spins; accordingly, T2 is known as the spin-spin relaxation time.
The equilibration of the transverse magnetization is an exponential
decay process; for example, after application of a 90º excitation
pulse, the transverse magnetization decay as a function of time in
the setting of very long TRs (Figure 2) is approximated by the
(See Equation 3.)
As in the case of T1, this equation can be rearranged with basic
algebraic manipulations resulting in the following:
(See Equation 4.)
Hence, if the logarithmic quantity in the left-hand side is
plotted as function of time, a straight line is predicted.
Furthermore, the slope of this line is equal to the inverse of T2.
This is the basis of Q-MRI algorithms for estimating T2 with
multi-spin-echo experiments. Again, a minimum of only 2 points (ie,
2 echo times) are required to determine the slope of this line, and
hence T2, though more measured points result in a more accurate
slope estimation with noisy data.
Proton density quantitative MR imaging
When TR is very long and TE (time to echo) is very short, the MR
signal is directly proportional to the unweighted number of
spinning protons present in the scanned volume. Images acquired
with such a technique are minimally weighted by the relaxation
times and are, therefore, termed PD weighted. Thus, the PD of each
voxel forms the base image matrix upon which T1 weighting (by
shortening TR) and T2 weighting (by prolonging TE) add contrast
information. Proton density is proportional to, and according to
Equation 1 or 3, can be quantified together with T1 or T2,
respectively, as the extrapolated value of the transverse
magnetization in the limit of infinitely short TE (ie, the y-axis
intercepts in Figure 1B and 2B at a time of 0 msec).
Quantitative MR imaging pulse sequences
Many Q-MRI pulse sequences based on the differential weighting
principle have been described in the literature. T2 differential
weighting is commonly obtained via multi-echo imaging while partial
saturation and inversion recovery (IR) have been used for T1
differential weighting. Some interrogate slices at many relaxation
time points while some use the theoretical minimum of 2 time
points. Almost all MR signal types have been used including
gradient echoes, spin echoes, and hybrid readout methods (fast or
turbo spin echo and echoplanar imaging).
Many of these Q-MRI pulse sequences target a single relaxation
parameter, but a few are capable of targeting multiple parameters
(T1, T2, and PD) in a single scan. Some described Q-MRI pulse
sequences interrogate 1 slice per scan and others provide volume
As with MRI in general, increasing the scanning speed of Q-MRI
is of paramount importance for clinical acceptance. The main
roadblock to faster Q-MRI has been the loss of quantitative
accuracy possibly associated with increasing imaging speed.
Possible sources of error include imperfection of RF pulses in
multislice imaging, interslice crosstalk, magnetization transfer
effects, and computational inaccuracies from using a reduced number
of time points with real data that, in general, contains varying
levels of noise. The theoretical "gold standard" Q-MRI pulse
sequences are fully relaxed (ie, infinite TR), are single-slice,
and interrogate tissues at an infinite number of relaxation time
points. To illustrate the slowness of such an approach, to generate
one 256 Z 256 T2 map with a multi-spin-echo sequence operating at
8-second TR, a scan time >34 minutes results.
Quantitative maps of T1, T2, and PD are not the only end
products of Q-MRI. These data-rich maps may be further processed
using a wide variety of approaches to yield information that may be
more clinically useful. Computer postprocessing of Q-MRI data is a
natural next step in data interpretation and may involve techniques
such as segmentation, volumetry, structural analysis, and the
generation of MR images with computer-synthe-sized T1 and T2
contrast weightings (Figures 6 and 7).
Q-MRI maps may be used as source data for semiautomated or
automated segmentation into organs or tissue types based on MR
Particular voxel subsets may be chosen from a multiaxis plot of
values such as T1, T2, and PD (Figure 3). Voxel spatial
relationships may also be combined with Q-MRI relationships to aid
in anatomic segmentation (Figure 4). Segmentation serves as an
intermediate step in quantification of organ volumes as well as in
generation of frequency histograms. Frequency histograms may also
be generated from the entire scan data set or segmented subsets of
organs or tissue types (Figure 5).
Weighted combinations of co-registered Q-MRI maps may be used to
create synthetic MR images that mimic directly acquired images
(Figures 6 and 7).
Though these image sets may resemble their traditional MRI
counterparts, they differ significantly in that the radiologist may
vary the degree of T1, T2, PD, and IR weighting at the time of
reading. The most tangible benefit to this type of imaging would be
the enormous potential time savings possible in replacing multiple
pulse sequences in a conventional MR examination with a single
Q-MRI pulse sequence. Relative weighting may be varied analogous to
windowing and leveling in a CT study.
Clinical applications of relaxometric quantitative MR
imaging: A review
Q-MRI techniques that are becoming mainstream in current
clinical practice include diffusion and perfusion in the setting of
cerebral ischemia and infarction. Although these techniques are
quantitative, in current clinical practice, the information is
usually interpreted in a subjective manner using visual inspection
of the maps to detect relative differences in pixel brightness (eg,
apparent diffusion coefficient [ADC] and perfusion maps) in much
the same way directly acquired images are interpreted.
Though applications of Q-MRI specific to quantification of T1,
T2, and PD have been discussed in the scientific literature, they
have not yet found routine use in clinical practice. A review of
promising clinical applications follows.
As with many early MRI techniques, one of Q-MRI's first
demonstrations in humans was in the brain. As an examination that
is less prone to motion artifact than imaging of other body parts,
quantification of relaxation times in gray and white matter as well
as cerebrospinal fluid was an attractive initial application for
the Q-MRI technique. Almost all Q-MRI pulse sequences have been
tested in the brain showing the normal QMRI brain architecture.
A complete review is outside the scope of this paper and can be
found in the book edited by Tofts.
Pathological deviations studied with Q-MRI include the effects of
iron deposition in patients with Parkinson's disease,
abnormal Q-MRI measures in multiple sclerosis plaques,
as well as cerebral edema related to stroke.
Q-MRI relaxometric studies of patients with schizophrenia
and with human immunodeficiency virus infection
have also been published.
Q-MRI brain postprocessing applications include generation of
as well as segmentation, quantification, and characterization of
tissue types, such as gray matter, white matter, and cerebrospinal
These methods have also been applied to the human orbit with
separation of extraocular muscles and retrobulbar fat from the
Synthetic MR images in the brain have been generated by multiple
groups using Q-MRI acquisition techniques with close resemblance to
directly acquired images.
Abdominal imaging (liver, spleen)
Another application in clinical practice includes the
characterization of liver lesions. T1 and T2 relaxation times
measured by echoplanar methods have been shown to be helpful in the
evaluation of focal lesions.
Dual-echo T2 techniques using traced regions of interest have also
proved to be more accurate than conventional qualitative visual
methods in differentiating benign from malignant foci.
These techniques have not found widespread use, however, perhaps
due to the perceived complexity of relaxation time calculation.
The amount of hepatic iron deposition in diseases such as
primary and secondary hemochromatosis has been repeatedly shown to
correlate closely with T2 and T2* relaxivity.
Q-MRI may be used not only to determine the severity of iron
deposition, but also to monitor response to medical therapy.
Other diffuse liver diseases that may benefit from Q-MRI analysis
include steatosis, hepatitis, and cirrhosis; however, further work
is needed to determine Q-MRI efficacy in these disease
As in the brain and orbit, synthetic MR images of the liver and
spleen have also been generated with the same capacity for the
radiologist to vary T1, T2, and IR weighting at the time of image
Pelvis (prostate, uterus)
Q-MRI has been applied to both the male and female pelvis for
both prostate and uterine imaging. Fast Q-MRI imaging of the
prostate has met with some success, especially in the measurement
of water content and its correlation with citrate concentration in
predicting prostate cancer.
QMRI techniques have also been used recently to measure T1 and T2
relaxation times of the normal female uterus at 1.5T and 3.0T.
Thorax (lung, heart, and breast)
Lung T1 relaxation times and changes in T1 with oxygenation have
been shown by using snapshot fast low-angle shot (FLASH), a
gradient-echo pulse sequence.
At least one study of lung T2 relaxation time has been performed ex
vivo in juvenile pigs.
Most quantitative work being performed in the thorax, however,
has concentrated on the myocardium. T2 maps have been generated in
vivo (human) and T2* maps ex vivo (beating rat hearts) in attempts
to correlate T2 and T2* prolongation to decreased oxygen
microcirculation and ischemia with good result.
T1 relaxation times of myocardium have also been measured and
mapped in healthy hearts as well as in myocardial infarction.
Quantitative approaches to contrast kinetics have also been
described by multiple groups for use in evaluating myocardial
enhancement as well as contrast enhancement in breast imaging.
TurboFLASH and T1 fast-acquisition relaxation mapping (T1 FARM)
pulse sequences have been used to successfully quantify myocardial
perfusion via measured changes in T1 relaxivity.
The FLASH pulse sequence has also been used to acquire T1 maps of
the breast before and after contrast administration to calculate a
concentration-time curve and potentially improve breast MR
Fetal/pediatric (brain development, lung maturity,
Q-MRI techniques have also found uses in fetal and pediatric MR
imaging of developing organs. Much of the early neuroradiologic
Q-MRI research focused on myelin characterization of the developing
fetal and pediatric brain through measurements of T1 relaxation
time in white matter showing a clear relationship between the time
course of T1 relaxivity changes with age.
T1 relaxation times were also shown to be significantly different
from controls in children with sickle cell disease (significantly
higher before the age of 2 years and significantly lower by the age
of 4 years).
Both T1 and T2 measurements have been made in vivo in the
preterm human placenta showing significant decrease in T1
relaxation times in placentas of compromised pregnancies
(pre-eclampsia and intrauterine growth restriction) compared with
times in those of controls. This has been postulated to be due to
placental infarction and fibrosis.
A similar in vivo assay has been applied to measurements of fetal
lung maturity, showing a relationship of both T1 and T2 to
gestational age and lung volume.
The implications for these studies include potential noninvasive
quantitative approaches to measuring fetal health.
Musculoskeletal (bone marrow, cartilage)
Various Q-MRI approaches have been used to characterize marrow
lipid and trabecular bone in the human skeleton. Estimates of
marrow lipid content have been made with line scan spin-echo
techniques (both conventional and fast spin echo).
Gradient-echo sequences have also been applied to marrow lipid to
These T2* measures correlated well with dual energy X-ray
absorptiometry bone mineral density measurements, indicating that
marrow T2* relaxation may be correlated to trabecular bone content.
Distribution histograms have also been generated from T1 and T2
measures of bone.
Ex vivo and in vivo measures of T1 and T2 for skeletal muscle
were attempted using both NMR spectroscopy as well as MRI as early
In a later experiment, in vivo T2 measures were shown with
multicomponent T2 histograms of at least 4 differing populations of
protons in the flexor digitorum profundus.
Applications in cartilage have included spin-echo measures of T2
in human cartilage.
T2 times increase with early osteoarthritis and then decrease with
more severe osteoarthritis. T2 maps have also shown significant
intercompartment and intracompartment variability, reflecting focal
cartilage defects seen in early osteoarthritis.
While the concept of using magnetic resonance as a quantitative
tool predates the development of MR imaging, the clinical practice
of MR imaging has been predominantly qualitative for much of its
history. With the ongoing development of more powerful and precise
scanner and computer hardware, as well as innovations in fast pulse
sequence design, Q-MRI is rapidly becoming clinically feasible. T1
and T2 relaxation times and PD may be measured and mapped with a
variety of pulse sequences, including ones that measure all 3
properties simultaneously. Use of coregistered maps of T1, T2, and
PD may be further postprocessed for segmentation and volumetry,
generation of distribution histograms, as well as derivation of
synthetic MR images. An exciting potential future application
utilizing Q-MRI postprocessing may even include design of
computer-aided detec-tion/diagnosis tools. Q-MRI techniques have
already been shown in many organ systems throughout the human body
in an effort to improve diagnostic sensitivity as well as monitor
therapy. As these methods employ conventional MR scanning
equipment, Q-MRI shows the potential for widespread adoption in
clinical practice as well as the promise of more automated and
efficient MR image processing.