Imaging of Oxygen Transfer Among Microvessels of Rat
Cremaster Muscle
Hirosuke Kobayashi, MD, PhD; Naosada Takizawa, PhD
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Background—The proximity of capillaries, arterioles, and venules provides complex spatial relationships that lead to
oxygen transfer among microvessels. Although a conceptual image of complex oxygen transfer among microvessels has
been hypothesized, in vivo mapping of oxygen saturation (SO2) levels in microvessels had never been performed.
Methods and Results—The oxygen profile of the arterioles and venules of the rat cremaster muscle during normoxia and
hypoxia was visualized by preparing pseudo-color images of SO2 levels based on microspectrophotometry data obtained
by using 3 different optical filters and a cooled CCD camera. The SO2 images showed lower SO2 levels in arterioles close
to their walls, and the SO2 levels in the paired venules showed higher SO2 levels close to the arterioles. There were
capillaries that crossed the microvessels whose SO2 levels changed as they crossed the microvessels. The SO2 levels were
lower close to the vessel wall than in the centerline level of the microvessels, and the highest SO2 levels in venules
paralleling arterioles were skewed toward the arterial side. The SO2 images showed that the SO2 level in arterioles
decreased after crossing venules, whereas the SO2 level in venules increased after crossing arterioles.
Conclusions—Visualization of intravascular SO2 levels suggested that oxygen is transferred between paired microvessels
and between crossing microvessels in rat cremaster muscle. The possibility that oxygen is transported from some
arterioles to venules and tissue through adjacent capillaries is proposed. (Circulation. 2002;105:1713-1719.)
Key Words: imaging 䡲 microcirculation 䡲 oxygen 䡲 muscles
P
revious studies have shown oxygen transfer from precapillary vessels to the tissues and into postcapillary vessels,
as well as oxygen transfer among microvessels.1–9 Because
the walls of vessels in the microcirculation are permeable to
oxygen, the proximity of capillaries, arterioles, and venules
provides complex spatial relationships that lead to oxygen
transfer among the microvessels. Although a conceptual
image of complex oxygen transfer among microvessels has
been described,10 –11 in vivo oxygen saturation (SO2) mapping
of microvessels had never been performed.
In most previous in vivo studies, microphotometric measurements were made at the center of microvessels just before
the bifurcation, with the assumption of thorough mixing of
the blood before the bifurcation and homogeneous distribution of SO2. Mott et al12 applied a newly developed optical
triplicator for intravital video microscopy of oxygen saturation and reported findings of intravascular cross-sectional
nonuniform oxygen saturation profiles, indicating the presence of luminal gradients in SO2.
We obtained 3 microvascular images with 3 different
optical filters and reconstructed images of SO2 in cremaster
microvessels based on the 3 images. Because the SO2 images
in microvessels were very complex, we focused on (1) spatial
relationships in oxygen transfer between microvessels, particularly between paired arterioles and venules and between
crossing (overridden and overriding) vessels, and (2) the
intravascular cross-sectional SO2 distribution in paired
microvessels.
Methods
Animals
Animal care was in accordance with the guidelines of the Animal
Care Committee of Kitasato University. Six male Wistar rats (Nihon
SLC, Shizuoka, Japan) were intraperitoneally anesthetized with 1 g/kg
urethane, intubated, and ventilated. An arterial catheter was introduced
into a carotid artery to monitor mean arterial pressure (MAP). Data were
collected only when 130 mm Hg⬎MAP⬎90 mm Hg during normoxia
and 120 mm Hg⬎MAP⬎70 mm Hg at FIO2 0.12. Rectal temperature
was monitored and maintained at 37.0⫾1.0°C with the use of a warm
plate. The cremaster muscle was exposed and spread out according to
Baez13 and then fixed on a transparent illumination stage (Microwarm
plate DC-MP-300DM, Kitasato Supply) heated to 37°C. The muscle
was covered with gas-impermeable film (Saran).
Apparatus and Calculations for SO2 Imaging
Images were obtained by using a cooled charge-coupled device
(CCD) camera (a 19⫻19-␮m CCD chip with 512⫻512 pixels:
TH7895B, Thomson CSF; cooling camera head: CH250, Photometrics) installed on a microscope (BH2, Olympus Optics) with a
long–working-distance objective lens (SPlan x4/0.13, Olympus Optics). Samples were transilluminated through a long-distance focus
condenser (BH2-CD, Olympus Optics) by a halogen lamp (12V/
100W Olympus Optics) stabilized with an AC voltage stabilizer
Received December 31, 2001; accepted January 31, 2002.
From the Department of Medicine (H.K.), School of Medicine, and Information Science Center (N.T.), Kitasato University, Kanagawa, Japan.
Correspondence to Hirosuke Kobayashi, MD, PhD, Department of Medicine, Kitasato University School of Medicine, Kitasato 1-15-1, Sagamihara,
Kanagawa 228-8555, Japan. E-mail [email protected]
© 2002 American Heart Association, Inc.
Circulation is available at http://www.circulationaha.org
DOI: 10.1161/01.CIR.0000013783.63773.8F
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Circulation
April 9, 2002
(model SR-1010, Yutaka electric MFG). Three different filters,
having maximum transmission wavelengths of 521 nm, 546 nm, and
555 nm with about 5 nm of halfwidths at half-maximum, (ASC
optical filters, Asahi Bunko) were prepared. Each image signal
through each optical filter was accumulated for 1 second, and the
image in the CCD camera was sampled through an interface (AT200,
Photometrics) and transferred to a host computer (Model B132L,
Hewlett Packard) for further numeric calculations to obtain the SO2
image.
After adjusting for slight positional differences among the 3
images by maximizing cross-correlation of the images, we calculated
SO2 at each pixel of the CCD camera image, using the method of
Pittman and Duling14 –15 with minor modifications to take into
account the transmission profile of each optical filter, because light
passes through the filter not only at the peak transmission wavelength, but over a range of adjacent wavelengths (see Appendix for
a detailed description). We deleted SO2 values with low signal levels
when the corresponding optical path length was ⬍5 ␮m, and showed
the pixel as a white spot on the image.
Validation of the Method
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In Vitro Validation
Blood was obtained from male Wistar rats with a heparinized syringe
and equilibrated with a gas mixture of 30% O2 and 5% CO2 with N2
balance or a gas mixture of 5% CO2 with N2 balance by using a
tonometer (IL237, Instrumentation Laboratory) for 30 minutes. We
used 2 different types of chambers to validate our method. One was
a 0.1-mm-thick gas-tight transparent chamber. After introducing the
oxygenated or deoxygenated blood into the chamber, we then
confirmed a 100% SO2 homogeneous image for fully oxygenated
blood and a 0% SO2 homogeneous image for fully deoxygenated
blood. The estimated absorbance (see Appendix) was identical to the
observed absorbance.
The other chamber was composed of 2 glass slides, with a
150-␮m-thick coverglass placed between them at one end and the
other ends touching. The open sides between the slides were sealed
with hard wax. We then checked the influence of the thickness of the
blood layer on the SO2 measurements, and the thickness of the blood
layer had no effect on the SO2 values.
In Vivo Validation
When resting (not stretched) cremaster muscle not covered with
Saran was exposed to pure oxygen, the SO2 in the microvessels was
100%. By euthanizing rats after ventilation with pure nitrogen and by
superfusing the cremaster muscle with dithionite solution, SO2 in the
microvessels became 0%. To investigate changes in intravascular
SO2 after a change in tissue PO2, we placed a particle of sodium
hydrosulfite onto the muscle tissue ⬇200 ␮m from an arteriole. The
SO2 level decreased ⬇5 minutes after spot application of the sodium
hydrosulfite.
Figure 1. Inhomogeneous intravascular SO2 levels in paired
microvessels. In paired arterioles and venules, SO2 levels on the
venous side of the arterioles (a) were lower than in the centerline, and SO2 levels on the arterial side of venules (v) were higher
than in the centerline. Bar⫽100 ␮m.
catheter, and capillaries crossing paired microvessels were photographed using a blue-range excitation filter coupled with an emission
filter (BP495 and DM505, respectively, Olympus Optics).
Statistical Analysis
Values are expressed as means⫾SD. The Wilcoxon paired signed
rank test was used to detect statistically significant differences
between the SO2 levels in microvessels and between the peak SO2
position and centerline in microvessels.
Results
Intravascular SO2 Profile of Paired Microvessels
The SO2 images of paired arterioles and venules showed that
the SO2 levels on the venous side of the arterioles were lower
than in the centerline and that the SO2 levels on the arterial
side of venules were higher than in the centerline (Figure 1).
Cross-Sectional SO2 Profile in Paired Microvessels
Two adjacent pixels of an SO2 image were averaged and these values
were further averaged along the vascular axis for 200 ␮m in an
attempt to reduce fluctuations in SO2 values. The cross-sectional SO2
profile thus was calculated. It should be noted that oxygen redistribution within the lumen in the radial direction might change the
radial SO2 profile along the longitudinal axis, but we evaluated the
radial SO2 profile averaged along this axis.
SO2 Images of Microvascular Architecture
To obtain an overall view of the SO2 levels in microvascular
architecture, SO2 images were pasted together one by one, and the
SO2 levels in microvascular architecture were reconstructed.
Visualization of Capillaries Crossing
Paired Microvessels
One milliliter of 5g/dL FITC-albumin (Sigma) dissolved in normal
saline was injected into the anesthetized animals via the arterial
Figure 2. Capillaries crossing paired microvessels. Some capillaries were visible on the arterioles and venules as lines, and
each line on the arterioles corresponded to a line on the venules
(see arrowheads), indicating crossing capillaries. Bar⫽100 ␮m.
Kobayashi and Takizawa
Oxygen Transfer Among Microvessels
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Figure 3. Cross-sectional SO2 distribution. The intravascular SO2 profiles were
inhomogeneous, and the SO2 levels were
considerably lower close to the vessel
walls than in the centerline. The SO2 profiles of the venules were skewed toward
the vessel wall on the arterial side. a
indicates arterioles; v, venules.
Some capillaries were visible on the arterioles and venules as
lines, and each line on the arterioles corresponded to a line on
the venules, indicating crossing capillaries (Figure 2).
The cross-sectional SO2 distribution showed inhomogeneous intravascular SO2 profiles, with intravascular SO2 levels
close to the vessel wall being lower than in the centerline
(Figure 3). The SO2 profiles of the venules were skewed
toward the vessel wall on the arterial side (Figure 3).
The peak SO2 level was higher (P⬍0.05) than the vessel
wall SO2 on either side of the arterioles, the same as in the
venules, but the wall inner surface SO2 levels on both sides
did not differ. The peak arteriolar SO2 level was higher than
the peak venular SO2 level (P⬍0.05). The position of the peak
SO2 in the venules was not in the centerline (P⬍0.05) but was
significantly closer to the vessel wall on the arteriolar side
(P⬍0.05) (Table).
Oxygen Transfer at Crossing Microvessels
The SO2 levels in venules increased after crossing arterioles
with higher SO2 levels, and the SO2 levels in arterioles
decreased after crossing venules with lower SO2 levels (Figure
4). The SO2 levels in upstream venules were low and then
increased after joining other venules with higher SO2 levels.
The SO2 levels in upstream venules located close to an
arteriole for a long distance were higher and decreased after
joining other venules with lower SO2 levels, but increased
again after crossing an arteriole with a higher SO2 level,
whereas the SO2 levels in upstream arterioles were high and
decreased after crossing venules (Figure 5).
SO2 Level in Microvascular Architecture
The SO2 levels in microvessels changed along the vessels
when they crossed other microvessels or were located close to
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April 9, 2002
SO2 Levels in Microvessels
Arterioles
(Inner Diameter⫽47.1⫾21.0 ␮m; n⫽6)
Venules
(Inner Diameter⫽61.9⫾15.9 ␮m; n⫽6)
Wall SO2 (1),
%
Peak SO2,
%
Wall SO2 (2),
%
Peak Position,
%
Wall SO2 (3),
%
Peak SO2,
%
Wall SO2 (4),
%
Peak Position,
%
71.6⫾9.9
89.6⫾6.0*†
72.8⫾8.9
56.4⫾22.1
53.2⫾15.2
67.0⫾10.9*
39.6⫾10.6
21.0⫾6.1‡
Values are means⫾SD. Wall SO2 is the SO2 level at the inner surface of the arteriolar wall on the far side (1), or the near side (2)
of its paired venule and at the inner surface of the venular wall located on the near side (3), or the far side (4) of its paired arteriole.
Peak position is the position of the peak SO2 level expressed as a percentage of the distance from the inner surface of the vessel wall
on the paired microvessels side to its total diameter (100%). The peak SO2 level was higher (*P⬍0.05) than the vessel wall SO2 on
either side of arterioles as well as venules. The peak arteriolar SO2 level was higher than the peak venular SO2 level (†P⬍0.05). The
peak SO2 position in venules was not in the centerline, but closer to the vessel wall on the arteriolar side (‡P⬍0.05).
other microvessels, and the intravascular SO2 levels were
inhomogeneous (Figure 6).
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Visualization of Capillaries Crossing
Paired Microvessels
Capillaries crossed paired microvessels, particularly at the
second- and third-order microvessels (Figure 7).
Discussion
The intravascular cross-sectional SO2 profiles and SO2 images
of microvessels indicated that SO2 declined toward the vessel
wall. Previous studies1– 4,16 showed that during normoxia, SO2
or PO2 decreased downstream in arterioles, indicating a large
oxygen efflux from the arterioles. The high rate of oxygen
loss and uniformly lower values of blood SO2 near the arterial
wall indicate a substantial oxygen efflux from the arterioles.
However, there has been controversy as to where the oxygen
driven by this intravascular PO2 gradient goes.
Figure 4. Oxygen transfer at crossing microvessels. The SO2
levels in venules (v) increased after crossing arterioles (a) with
higher SO2 levels, whereas the SO2 levels in arterioles decreased
after crossing venules with lower SO2 levels. Bar⫽100 ␮m.
The oxygen disappearance rates measured in precapillary
microvessels in vivo have been reported to be much higher
than the theoretical estimates.17 One possible explanation for
this is a high oxygen consumption rate of endothelial
cells16,18; however, a theoretical study19 based on a large body
of previous reports on endothelial metabolism and oxygen
consumption failed to demonstrate a high oxygen disappearance rate from microvessels. Another possibility is overestimation of the oxygen efflux rate related to the assumption on
which the estimate of convective oxygen flow was based, ie,
the assumption of cross-sectional uniformity of hemoglobin
concentration and SO2 within microvessels,11 especially because intravascular SO2 is inhomogeneously distributed, with
a high centerline level and low level near the vessel wall, as
shown by Mott et al12 and in our present study. However,
whether a more accurate estimate of the rate of oxygen
disappearance results in lower values for oxygen efflux rates
has never been evaluated.
Earlier observations5,8 showed that venous SO2 can be
higher than capillary SO2. Our previous study9 showed that
during normoxia, SO2 in venous vessels paralleling arterioles
was increased toward downstream (central) vessels. In our
present study, the highest cross-sectional SO2 levels in
venules paralleling arterioles were skewed toward the arterial
side, and the SO2 images in the venule showed higher SO2
levels close to the paired arterioles. These findings suggest
arterio-venous oxygen transfer.
Although several lines of evidence have indicated that
oxygen is transferred from arterioles to their paired venules,
it is not obvious whether the oxygen transfer is solely
diffusive. Some arterial and venous vessels are ⬎100 ␮m
apart, and diffusive oxygen transfer between these microvessels is unlikely. A mathematical model of paired arterioles
and venules indicated that diffusive counter-current oxygen
exchange would not normally be a significant effect.20
There were several capillaries crossing some microvessels.
The SO2 images of the paired microvessels and the changes in
SO2 levels in the arterioles and venules with crossing capillaries suggest that these adjacent capillaries contributed to
oxygen transfer between paired microvessels. It is possible
that when capillaries cross an arteriole and then its paired
venule, oxygen is transferred by diffusion from the arteriole
to the capillaries, by convection in the capillaries, and
subsequently by diffusion from the capillaries to the paired
venule. These oxygenated crossing capillaries run closest to
Kobayashi and Takizawa
Oxygen Transfer Among Microvessels
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Figure 5. A magnified view of SO2
levels in crossing microvessels. The
SO2 level in the upstream venule
(v3) was low, and increased (see
v1) after joining another venule with
a higher SO2 levels (v2). The SO2
level in the upstream venule (v4)
located close to an arteriole (a1)
was high, and decreased (see
upstream v2) after joining venule
with a lower SO2 level (v5), but
increased (see downstream v2)
again after crossing an arteriole
with a higher SO2 level (a1). The
SO2 level in the upstream arteriole
(a1) was high, but it decreased
after crossing a venule (v2).
Bar⫽100 ␮m.
the venules at the centerline of the venules (at the top or the
bottom of the venules), and oxygen begins to be transferred
from capillaries to venules before the centerline of the
venules, resulting in a higher SO2 level just before the
centerline.
The idea that oxygen loss by arterioles to adjacent capillaries might contribute to the high rate of oxygen loss by
arterioles was explored theoretically in previous studies.21–23
Secomb and Hsu23 used a 3-dimensional configuration of
capillaries and arterioles in a cuboid tissue region to simulate
oxygen transfer from microvessels to tissue; they found that
diffusive oxygen loss from arterioles equaled ⬇85% of
consumption in the tissue, and that crossing capillaries
absorbed much of this oxygen (⬇45% of consumption) and
delivered it at downstream locations. Thus, diffusive oxygen
transfer from arterioles to capillaries seemed to play an
important role in distributing oxygen throughout the tissue.
Accordingly, it is theoretically and experimentally likely
that a considerable part of the oxygen that left some arterial
microvessels was transferred to crossing capillaries and was
carried by the capillaries to venules and tissue.
Oxygen transfer from arterioles to crossing venules was
also shown in this study, and thus it is likely that crossing
microvessels reduce the barrier to diffusional oxygen transfer,
making intervascular oxygen transfer easier. Oxygen would
transfer from normoxic arterioles to hypoxic venules, and the
venule would in turn become normoxic and would provide
oxygen to the tissues.
In conclusion, the intravascular SO2 images suggested
oxygen transfer among microvessels in muscle. We propose
Figure 6. SO2 levels in microvascular architecture.
The SO2 levels in microvessels changed along the
vessels, and the intravascular SO2 levels were inhomogeneous in paired vessels and in crossing
microvessels. Bar⫽1 mm.
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Circulation
April 9, 2002
the transmitted light intensity through fully deoxygenated unit blood
layer, qdeoxyi, is expressed as,
(4)
冕
⬁
qdeoxyi⫽
qdeoxy共␭兲䡠Fi共␭兲d␭
␭⫽0
When ⑀oxy(␭) and ⑀deoxy(␭) are molar extinction coefficients of the
fully oxygenated and fully deoxygenated blood unit, respectively, at
a wavelength ␭, we obtain
(5)
⑀ oxy共␭兲⫽log10共r共␭兲/qoxy共␭兲兲
and
(6)
⑀ deoxy共␭兲⫽log10共r共␭兲/qdeoxy共␭兲兲
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Figure 7. Capillaries were crossing paired microvessels (2°A
and 2°V microvessels in this case). Bar⫽100 ␮m.
Combining Equations 3 and 5, and combining Equations 4 and 6,
we obtain
the possibility that a considerable part of the oxygen that
disappears from some arterioles is transferred to venules and
tissue through adjacent capillaries.
(7)
冕
⬁
关r共␭兲䡠Fi共␭兲/10⑀oxy共␭兲兴d␭
qoxyi⫽
␭⫽0
and
Appendix
An image file was obtained using each of 3 optical filters i (1, 2, or
3). The peak transmission wavelengths (␭i) of the filters were:
␭1⫽521 nm, ␭2⫽546 nm, and ␭3⫽555 nm. The transmission profile
of each optical filter, Fi(␭), was measured. Fi(␭) was defined as the
ratio of the transmitted photon number to inlet photon number at the
wavelength of ␭. Each image file obtained using the optical filter, i,
was expressed as Mi{mi,j}i⫽1,3, where mi,j is the number of photons
captured at a CCD element of j in 1 second. The subscript j indicates
the location on the CCD chip, and the CCD elements consisted of
512 columns and 512 rows, the element j therefore ranging from 1 to
262 144. The photon number of each element in 1 second was stored
as a 16-bit digit.
In order to obtain an SO2 image, S{sj}, where sj is the SO2 level at
each element j, we captured 3 reference (blank) images, Ri{ri,j}i⫽1,3,
using each optical filter i without specimen. The observation field
was homogeneously illuminated by the Köller illumination system
with an AC voltage stabilizer. As a result, the density of each
reference image was flat, and Ri{ri,j}i⫽1,3 was expressed as Ri{ri}i⫽1,3.
We then obtained 3 images, Mi{mi,j}i⫽1,3, using each optical filter, of
rat cremaster muscle with microvessels.
Each element of the absorbance image, Ai{ai,j}, using an optical
filter, i, was then calculated as follows:
(1)
ai, j⫽log10共ri/mi, j兲
The extinction coefficients of both oxygenated and deoxygenated
blood using an optical filter, i, are influenced by the transmission
profile of the filter.
When the reference light intensity and the transmitted light
intensity through fully oxygenated unit blood (1 unit corresponds to
1 mol/L hemoglobin with 1 cm blood layer) at wavelength ␭ without
a filter are set at r(␭) and qoxy(␭), respectively, the reference light
intensity, ri, and the transmitted light intensity through the fully
oxygenated unit blood using a filter i, qoxyi, are expressed as,
(2)
冕
r共␭兲䡠Fi共␭兲d␭
ri⫽
␭⫽0
冕
⬁
qoxyi⫽
qoxy共␭兲䡠Fi共␭兲d␭
␭⫽0
Similarly, if the transmitted light intensity through fully deoxygenated unit blood at wavelength ␭ without a filter is qdeoxy(␭), then
冕
⬁
qdeoxyi⫽
关r共␭兲䡠Fi共␭兲/10⑀deoxy共␭兲兴d␭
␭⫽0
Using an optical filter, i, with a peak transmission wavelength of
␭i, the molar extinction coefficients of fully oxygenated and deoxygenated unit blood layer, Eoxyi and Edeoxyi, accounting for the filter
characteristic Fi(␭), can be obtained as,
(9)
Eoxyi⫽log10共ri/qoxyi兲
and
(10)
Edeoxyi⫽log10共ri/qdeoxyi兲
In our previous study9 we obtained ⑀oxy(␭) and ⑀deoxy(␭) and the
reference spectrum r(␭), and found that ⑀oxy(␭) and ⑀deoxy(␭) were
identical to previously reported values at several discrete wavelengths.24 Using these ⑀oxy(␭), ⑀deoxy(␭) and r(␭) values, Eoxyi can be
obtained by Equations 2, 7, and 9, and Edeoxyi by Equations 2, 8,
and 10.
The integration was performed by numerical integration with a
wavelength step of 0.56 nm, which was the resolution limit of the
spectrophotometry in our previous study, ranging ␭i ⫾28 nm,
because Fi(␭) was zero beyond this range. Eoxyi and Edeoxyi thus
obtained were:
(11)
Eoxy1⫽0.59 and Edeoxy1⫽0.50 at ␭1⫽521 nm
(12)
Eoxy2⫽0.95 and Edeoxy2⫽1.06 at ␭2⫽546 nm
(13)
Eoxy3⫽0.82 and Edeoxy3⫽1.09 at ␭3⫽555 nm
The absorbance (aj) at position j of a microvessel at wavelength ␭
is formulated as follows14 –15:
(14)
⬁
and
(3)
(8)
aj共␭兲⫽兵⑀oxy共␭兲䡠sj/100⫹⑀deoxy共␭兲䡠共100⫺sj兲/100其䡠cj⫹bj
where cj is the value of the hemoglobin concentration multiplied by
the mean optical path length at the measured pixel of the microvessel, bj is a scattering term, and sj is SO2 (%).
Applying a filter i and accounting for the transmission profile of
the filter, the absorbance at the position j obtained using filter i, ai,j,
can now be formulated as,
(15)
ai, j⫽兵Eoxyi䡠sj/100⫹Edeoxyi䡠共100⫺sj兲/100其䡠cj⫹bj
These 3 unknown parameters (sj, cj, and bj) at a position j could be
obtained by solving the 3 equations for i⫽1, 2, and 3. Therefore,
Kobayashi and Takizawa
(16)
⌬a1,2,j䡠⌬Edeoxy2,3⫺⌬a2,3,j䡠⌬Edeoxy1,2
sj
⫽
100 ⌬a1,2,j䡠共⌬Edeoxy2,3⫺⌬Eoxy2,3兲⫺⌬a2,3,j䡠共⌬Edeoxy1,2⫺⌬Eoxy1,2兲
where
⌬ai,k,j: ai,j - ak,j,
⌬Eoxy i,k: Eoxy i - Eoxy k,
and ⌬Edeoxy i,k: Edeoxy i ⫺ Edeoxyk
for i,k⫽1, 2, or 3.
This yielded the SO2 image, S{sj}.
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Hirosuke Kobayashi and Naosada Takizawa
Circulation. 2002;105:1713-1719; originally published online March 25, 2002;
doi: 10.1161/01.CIR.0000013783.63773.8F
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