Open Journal of Radiology, 2012, 2, 31-38
http://dx.doi.org/10.4236/ojrad.2012.21006 Published Online March 2012 (http://www.SciRP.org/journal/ojrad)
Quantitative Flow Relaxographic Angiography
1School of Energy, Environmental, Biological and Medical Engineering, University of Cincinnati,
2Department of Psychiatry and Behavioral Neuroscience, University of Cincinnati, Cincinnati, USA
3Center for Imaging Research, University of Cincinnati, Cincinnati, USA
Received January 15, 2012; revised February 17, 2012; accepted February 27, 2012
A powerful method, termed flow relaxography, allowing the practical and accurate determination of the water proton
MR signal relaxation time distributions has been recently introduced with a phantom, having both flowing and non-
flowing water. It was demonstrated that this method can discriminate the signals from the flowing and non-flowing
spins, since flow affects the apparent T1 (T) value. In this report, it is demonstrated that this technique is effective also
in the human leg in vivo. Flow relaxographic angiography is presented for the first time. This technique promises to
accomplish the twin goals of flow studies in medical MRI, to display vascular anatomy and measure its blood flow rate,
in the same image.
Keywords: Angiography; Relaxography; Blood Flow; T1 Measurement
Blood flow measurement and angiographic research re-
main very active. This is because blood flow is an impor-
tant physiological parameter for many vascular patholo-
gies. MRI promises to be an ideal method for noninva-
sively obtaining most vascular information. Develop-
ments in quantitative MR measurement of blood flow
can generally be placed in either of two branches—the
time-of-flight (TOF) and phase-contrast (PC) methods [1,
2]. The former is based on the inflow effect, as is the
approach  presented in this work. However, most TOF
methods provide for blood vessel visualization by sup-
pression the tissue signal and even partially the blood
1H2O signal and usually provide no direct quantitative
flow rate information . In contrast, the PC approach
relies on a very different phenomenon. This method ex-
ploits the change in transverse magnetization phase that
occurs when nuclear spins move along a magnetic field
gradient; a phenomenon first reported by Hahn in 1960
. The utility of the motion-induced phase shift for flow
detection was soon recognized by Moran  and many
methods based on PC have been proposed and demon-
By utilizing the magnetic tagging method, Singer was
the first to carry out NMR flow measurement on an in
vivo system, in 1959 . He demonstrated the blood flow
measurement in a mouse tail with a two-coil system cha-
racteristic of a TOF method. Later, he and coworkers
were also able to apply this technique to measure the
blood flow velocity in the human forearm and head [8,9].
At about the same time of the discovery of flow-affected
NMR, other studies also showed that the reciprocal 1H2O
value is sensitive to coherent motion and that
the change is linear with the water flow rate [10,11].
Later, others showed that the apparent transverse relaxa-
tion time (2
) followed the same behavior [12,13]. This
then has become one of the key concepts for the deve-
lopment of flow NMR , perfusion imaging [15-17]
and angiographic imaging [1,2]. Moreover, this techni-
que has been applied to the study of human brain activity
The NMR resonance frequency of a signal from a
flowing fluid is not different from that when it is station-
ary. Thus, the discrimination of the signals from flowing
and non-flowing spins is not possible in the Fourier do-
main. However, the flow of a fluid can change the ap-
parent relaxation time for the recovery of its NMR signal
after a perturbation of the nuclear magnetization from
equilibrium. Recently, we have shown that techniques,
termed longitudinal relaxography and relaxographic
imaging [23,24], which can quantitatively discriminate
isochronous NMR signals according to their 1
have potential in this area. We also applied this powerful
method for practical and accurate determination of re-
laxation time distributions that obtain for the NMR sig-
nals from a phantom having a mixture of flowing and
non-flowing water . We refer to this method as flow
opyright © 2012 SciRes. OJRad
relaxography and thus to the distribution as a flow re-
laxogram—the distribution of the 1 values and, con-
sequently, flow velocity values if flow relaxivity (r1F) is
known. Since flow affects the 1 value, it should allow
the discrimination of the signals from flowing and non-
flowing spins. Importantly, with spatial encoding, this
technique (i.e., flow relaxographic imaging) is suitable
for quantitative angiography, which we would like to
term f low relaxographic angiography. Unlike most other
existing angiographic techniques, this technique will al-
low us to display vascular anatomy and determine its
flow rate in the same image.
Thus, the aim of this study is to evaluate the feasibility
of this technique for the application of quantitative blood
flow parameter measurement in vivo. In this paper, we
apply this technique to the human leg vascular system.
All studies were performed with a 4T Varian whole-body
instrument. Four normal healthy male volunteers were
studied after giving their informed consents. Each subject
lay supine with his right thigh positioned inside a bird-
cage RF transceiver coil and supported and restrained
with forms. The transverse image slice was centered in
this coil and located about 8 cm above the knee. The
1H2O 1 distribution was determined with data ac-
quired using the PURR-TURBO pulse sequence .
Following a slice-selective adiabatic inversion pulse, 32
slice-selective 5° read pulses were applied and data were
collected immediately after each. The observe (read)
slice thickness (So) was fixed at 1.0 cm while the inver-
sion slice thickness (Si) was incremented from 1.5 cm to
12 cm (see below). All slab center planes were the same
as that of the RF coil: the slices are axial (i.e., in the XY
plane). The data matrix is (128)2, zero filled to (256)2 and
the nominal in-plane (XY) resolution in these images is
(0.55 mm)2. The inversion recovery time (TI) varied
from 48 ms to 5.3 s with spacing increasing geometri-
cally . The total acquisition time for this set of
PURR-TURBO images was 2.8 minutes. For the original
PURR sequence , this would have been about 12
minutes. In our phantom experiment , we discovered
how one can control the flow relaxivity, r1F, noninva-
sively. Thus, the human leg imaging experiment was
repeated six times, with different Si values, increasing
from 1.5 cm to 12 cm.
The generation of the longitudinal relaxation time dis-
tribution—the relaxogram —from a set of relaxation
data was accomplished using CONTIN (a non-parametric
continuous method) and by a three three-parameter fit-
ting algorithm (assuming a single-valued T1 for the sig-
nal from each pixel). Details of this pixel-by-pixel analy-
sis are given elsewhere [25,26]. The flow velocity and
consequently the flow velocity map, was produced on a
pixel-by-pixel basis using Equation (1) of reference 
and taking r1F as (Vi/2)–1, where the volume of magneti-
zation inverted, Vi, is Si·Ap (Ap is the in-plane pixel area;
3.03 × 10–3 cm2, here). Rewriting this as Equation (1)
here, we have:
where Fl represents the (linear) flow velocity through
each pixel in a vessel.
The volume flow rate (Fv) for a vessel can be obtained
by multiplying its mean flow velocity (one half of its
maximum flow velocity; for laminar flow) and cross-
sectional area (A) values. The quantity A is the vessel
cross-sectional area. This is derived from the following
relationships: Fl,m = 21 = 2Fv/A: where Fl,m and
are the maximum and average flow velocities, respec-
tively . These calculations were made using the In-
teractive Data Language software package (IDL; Re-
search systems, Inc.; Boulder, CO) software package.
Figure 1 illustrates a typical result obtained from one vo-
lunteer using a flow-sensitive PURR-TURBO sequence
with a 1.5 cm inversion slab and TE = 5 ms. The top dis-
plays the 32 the right thigh axial thigh images, obtained
during the recovery after an inversion pulse. The right
side of the image is the right side of the thigh (i.e., the
view is from a superior perspective). These images can
be considered to be “T1-weighted” images, in the general
sense . The TI value (in ms) is given under each im-
age. Muscle, fat and bone marrow tissue and vessels are
clearly visualized. With the exception of the fat and bone
marrow tissue, 1H2O magnetization is negative (inverted)
at small TI values, but the gray-scale display exhibits its
magnitude. As time progresses, the differential relaxation
becomes very obvious. The images made at the largest TI
values show little contrast. These are essentially spin-
density images and it is clear that water is rather uni-
formly distributed though out the thigh slice. The longi-
tudinal relaxogram at the middle of Figure 1 is a histo-
gram of all single voxel relaxograms for the entire image
slice and results from submitting these 32 images for
CONTIN analysis on a pixel-by-pixel basis. Note the
logarithmic abscissa axis. The relaxogram is plotted with
the equal area display , so that peak areas are plani-
metrically comparable. We can produce a relaxographic
image for any of the 64 bins along the computed re-
laxogram, or combinations thereof. After inspecting the
structure evident in the whole-slice relaxogram, we formed
relaxographic images for the T1 (really 1
T ranges 0.01 -
0.2 s, 0.2 - 0.6 s and 0.6 - 4.6 s and these are shown in
the bottom of Figure 1. It is quite apparent that the im-
age on the bottom left represents only blood water having
Copyright © 2012 SciRes. OJRad
Copyright © 2012 SciRes. OJRad
Figure 1. At the top are shown, 32 images obtained during the recovery of magnetization after an inversion RF pulse. The
recovery time values (in ms) are indicated under each image. The nominal in-plane resolution is (0.55 mm)2. At the middle is
a composite 1H2O longitudinal relaxogram (in logarithmic scale) representing data from every voxel in the entire image slice.
Below it, also shown relaoxgraphic images made from the indicated sections (T1 values ranges) of the entire relaxogram. They
illustrate naturally segmented images of tissues with different relaxation rate constants, as well as water with different flow
a large flow rate, mostly in the interior of larger vessel
lumens (the popliteal artery (PA) and vein (PV), as well
as two saphenous vessels (S1 and S2)); and the image on
the bottom right represents only muscle tissue. However,
the image in the bottom center is more complicated. It
consists of bone marrow and subcutaneous fatty tissues,
as well as blood water with a small flow rate. As we will
see below, the rings in this image most likely represent
the slow-flowing water near the vessel walls (i.e., vessel
lumen annuli). Of course, the sum of all relaxographic
images is the spin density image. It seems impressive
that a very small vessel (arrow) buried in muscle can be
also clearly visualized with relaxographic imaging, while
not be seen easily (if at all) in the original T1-weighted
Figure 2 center shows a stacked plot of the longitude-
nal relaxogram from the same subject, as a function of Si.
The relaxographic images (Si = 1.5 cm) of Figure 1 and
their associated relaxogram are duplicated at the bottom
of Figure 2 for comparison. Shown at the top of Fig-
ure 2 are the Si = 12 cm relaxographic images, which are
produced from the same T1 ranges as those of Figure 1.
It is clearly seen that stationary 1H2O remains at the same
T1 value regardless of the Si value. However, the T1 of
flowing 1H2O is shifted to smaller values as Si decreases.
The vessel with the greatest blood flow rate has the most
reduced T1 value. Although the T1 value changes, it is
important to note that the flow rate in each vessel does
Figure 2. Shown at the middle is a stacked plot of the 1H2O longitudinal relaxogram as a function of inversion RF pulse slice
thickness (Si). The majority of signal, which is from non-flowing muscle tissue water, remains unchanged as Si is altered; as
illustrated with a vertical line. However, a very small amount of signal is shifted to smaller T1 values as Si decreases. As
examples, the T1 changes for the popliteal artery (PA) lumen center and annulus are indicated. Relaxographic images (RIs)
made from the same sections (indicated) of the bottom (Si = 1.5 cm) and the top (Si = 12 cm) relaxograms are shown below
and above it, respectively. The RIs at the bottom are essentially duplicated from those in Figure 1. Comparison of the top and
bottom images clearly shows that RIs with the same T1 value range are quite different. The RI at the top left represents
essentially the noise in the case.
Copyright © 2012 SciRes. OJRad
J.-H. LEE 35
not change. For Si = 12 cm, the relaxographic image,
which has been windowed-up for clearness, from the
smallest T1 range is essentially the noise for this case.
The T1 value of the PA central lumenal 1H2O was deter-
mined from the relaxogram at each Si value. These are
indicated on the stacked plot. Also, a line is drawn con-
necting the T1 values of the PA annular lumenal 1H2O at
the largest Sis and that at 1.5 cm. The behavior observed
helps confirm the assignment to water in the lumen an-
Figure 3 depicts plots of 1 as functions of 2(Si)-1
for one pixel from each vessel seen in Figure 1 and the
average 1 from 40 pixels selected at random from all
muscle regions. The area of largest vessel, PV, contains
almost 50 pixels, that of the smallest vessel detected, S3,
contains almost 10 pixels. The 1 values are the recip-
rocals of the 1 values for pixels selected from ROIs
exhibiting the largest 1 values (i.e. the highest flow
rate) of each vessel. Since the muscle 1
R values are
quite uniform, we have chosen 40 pixels from muscle
areas; a few pixels each from each muscle type and av-
eraged their 1 values. The symbols represent data from
five different vessels—PA, PV, subcutaneous saphenous
veins (S1, S2, S3) —and muscle; from top to bottom, re-
spectively. The solid lines drawn through them result
from linear-least-squares (LLS) fittings. The root-mean-
square, χ, values for all vessels are greater than 0.95 ex-
cept for PA, for which it is 0.88. The slope value of each
line essentially represents the maximum flow velocity
(Fl,m) of each vessel. The volume flow rate (Fv, Ta ble 1)
for each vessel can be obtained by multiplying its mean
flow velocity (
F = F1,m/2) and its cross-sectional area
(A), which can be estimated from Figure 1 bottom center
image. The vessel flow velocities measured in this study
are quite reasonable and are in a very good agreement
with those obtained by other investigators [28,29]. The
flow rate of muscle water is of course essentially zero.
The left panel of Figure 4 shows a color flow velocity
map overlaid on a gray-scale anatomical image and the
right panel shows a 3D plot of the PA and PV flow pat-
terns. These were obtained by fitting the Si-dependent
1 data, on a pixel-by-pixel basis, with Equation (1). It
is clear that the colored pixels represent only flowing
water. We refer to the determination of the flow velocity
map as flow relaxographic angiography. The map dis-
plays vascular anatomy and vascular blood velocities
simultaneously and quantitatively. In the 3-D flow pat-
tern plot, the z-axis measures the linear flow velocity.
The contour lines in the xy plane represent the 5, 10 and
15 cm/s flow rates. The flow patterns for these vessels
are quite consistent with that of laminar flow.
Table 1 gives the measured cross-sectional area, the
mean flow velocity and the volume flow rate for each
vessel. It is interesting to note that for the vessels we can
see the sum of the venous volume flow rates is almost
equal to the arterial volume flow rate, which is physio-
logically expected. Thus, the data in Tab le 1 can serve as
a self-check for this technique. We also list for compari-
son the calculated average intrinsic T1 (1) values from
the ROIs indicated and their corresponding average
measured T1 (
) values. The former are obtained
from the average of the y-intercepts of the 1
dependencies for all pixels within each of the vascular
ROIs. The measured values were obtained for the same
ROIs with the non-slice-selective inversion PURR-
TURBO RF pulse sequence version.
We find it quite gratifying that this technique can differ-
Figure 3. Plots of the 2/Si-dependence of the maximum first-
order relaxation rate constant values obtained from single
voxels in the selected regions indicated. The symbols repre-
sent data from the popliteal artery and vein (PA, PV) and
saphenous vessels (Ss), as well as the average of 1H2O 1
values from muscles. The solid lines result from LLS fittings.
Figure 4. A flow relaxographic angiography map and the
corresponding flow pattern are shown. The left panel show s
the color-coded map superimposed on the gray-scale anato-
mic image of the same subject. On the right, the PA (the left
peak) and PV (the right peak) 3D flow patterns are pre-
sented. The three contour levels represent flow velocities of
5, 10, 15 cm/s, respectively.
Copyright © 2012 SciRes. OJRad
Table 1. Summary of the vascular and flow parameters and 1H2O T1 values.
Vessel PA PV S1 S2 S3 Muscle
Area (cm2) 0.14 0.16 0.045 0.038 0.031 N/A
F (cm/s) 9.0 5.3 4.6 3.5 0.8 0.04 +/– 0.01
Fv (mL/min) 76 51 12 8.0 1.5 N/A
T (s) 0.94 1.84 1.74 1.76 1.53 1.5
(NSS) (s) 0.68 1.61 1.55 1.45 1.18 1.4
rentiate in space not only water signals from different
tissues, but also from water with different flow velocities;
that is, to observe the flow velocity distribution (flow
patterns). We were also able to find the direct relation-
ship (i.e., flow relaxivity) between water flow velocity
and the relaxation rate constant. This allows us to convert
relaxographic images into flow relaxographic angiogra-
phic images, which display both vascular anatomy and its
velocity simultaneously (Figure 4). The sum of all re-
laxographic images is the spin-density image.
The flow rates determined in this study (Table 1) are
in good agreement with the analogous values obtained by
Wehrli et al.  and Holland et al. . The latter pa-
per reported Doppler ultrasound measurements of the
popliteal artery mean volume flow to be 72 mL/min (our
observation, 76 mL/min). Wehrli et al. used a selective
saturation-recovery spin-echo MRI method to measure
the femoral vein mean flow velocity to be 5.25 cm/s (our
measurement, 5.3 cm/s).
Another important determination in this study is that
of the T1 value of blood 1H2O, as if it was stationary in
vivo, the average reciprocal value of the vertical axis
intercept. As far as we are aware, this is the first time that
the blood 1H2O T1 has been extrapolated to this condition.
We have reported this in a flow phantom study . It is
conceivable that this value will not be the same as would
be measured for stationary blood in vitro. It is important
to note that the impossibly negative T1 vertical intercepts
of Figure 3 result from the single voxel data plotted
therein. When we analyze the average T1 value, 1,
for the entire lumen of each vessel, we obtain positive
intercepts . This Figure 3 result can be attributed to
insufficient magnetization inversion and/or greater flow
rates at some regions near the lumens center.
The 1 extrapolations also yield the interesting
observation that the value for the one artery studied (<1.0
s) is significantly less than those for 1H2O in the veins
observed (averaging 1.72 sec) . This is a rather a
surprising result, since we (and probably most investiga-
tors) would likely expect that their values should be very
similar. Although, Radda and co-workers have shown
that the state of blood oxygenation has a great impact on
the in vitro transverse blood 1H2O relaxation rate con-
stant at 1.5 T , it has a smaller effect on longitudinal
relaxation at 4.7T . This is because the change of the
blood bulk magnetic susceptibility (BMS) caused by al-
tering the deoxy-Fe concentration is significant, and
while T2 is quite sensitive to this T1 is not. The water
proton-iron electron dipolar (hyperfine) interaction is
very small. Radda’s group also showed that the haema-
tocrit value affects the 1H2O T2 values for oxygenated
and deoxygenated blood in different ways. The former
has a linear dependency caused by varying macromo-
lecular concentration, while the latter has a much larger
non-linear dependency because of the above mentioned
BMS effect . No evidence a haematocrit effect on T1
was shown. Even if it is true that T1 can be altered by the
haematocrit, the difference we observe does not prove
that the haematocrit is different between the blood in the
artery and veins we examined. Thus, the T1 difference
between the blood 1H2O in arteries and veins remains a
very interesting question to be addressed. Further inves-
tigations are clearly called for. Although Kauppinen and
co-workers show that increasing the deoxygenation (as in
veins) of in vitro blood does increase 1H2O R1 (i.e. de-
crease T1), so does increasing the partial pressure of O2
for blood that is already well oxygenated (as in arteries)
It is important to note that 1H2O T1 values in tissues
are larger at higher field than at lower field . Thus,
with a 4T instrument, one will have a better chance to
differentiate the NMR signals from flowing and non-
flowing 1H2O, since the T1 of the former is always shifted
to a smaller value, just as by a paramagnetic contrast
reagent . An important feature of the PURR family
of pulse sequences is that the TI values are exponentially
spaced , this provides us a highly dynamic range for
T1 measurement during the period the magnetization be-
comes fully recovered. It is impressive that a quite small
vessel (arrowhead) embedded in the muscle group can be
clearly visualized in the middle relaxographic image and
not be easily seen (if at all) in the original T1-weighted
images We can foresee a number of potential medical
applications of this technique. For example, the study of
vascular disease is obvious. It may also be possible to
apply it to tumor diagnosis because the blood flow in
tumor tissue is different than that in normal tissue.
In summary, we have demonstrated that the flow re-
laxographic angiography is also effective in an in vivo
system. And, as illustrated for the first time, it provides
Copyright © 2012 SciRes. OJRad
J.-H. LEE 37
the possibility to display vascular anatomy and measure
its blood flow rate on the same images—the twin goals
of medical MRI flow studies—in the same image.
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