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Decompression sickness (DCS) in divers is caused by bubbles of inert gas. When DCS occurs, most bubbles can be found in the venous circulation: venous gas emboli (VGE). Bubbles are thought to be stabilized by low molecular weight surfactant reducing the plasma-air surface tension (γ). Proteins may play a role as well. We studied the interrelations between these substances, γ and VGE, measured before and after a dry dive simulation. VGE of 63 dive simulations (21-msw/40-minute profile) of 52 divers was examined 40, 80, 120 and 160 minutes after surfacing (precordial Doppler method) and albumin, total protein, triglycerides, total cholesterol and free fatty acids were determined pre-and post-exposure. To manipulate blood plasma composition, half of the subjects obtained a fat-rich breakfast, while the other half got a fat-poor breakfast pre-dive. Eleven subjects obtained both. VGE scores measured with the precordial Doppler method were transformed to the logarithm of Kisman Integrated Severity Scores. With statistical analysis, including (partial) correlations, it could not be established whether γ as well as VGE scores are related to albumin, total protein or total cholesterol. With triglycerides and fatty acids correlations were also lacking, despite the fact that these compounds varied substantially. The same holds true for the paired differences between the two exposures of the 11 subjects. Moreover, no correlation between surface tension and VGE could be shown. From these findings and some theoretical considerations it seems likely that proteins lower surface tension rather than lipids. Since the findings are not in concordance with the classical surfactant hypothesis, reconsideration seems necessary.
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Copyright © 2015 Undersea & Hyperbaric Medical Society, Inc.
Relationships between plasma lipids, proteins, surface tension
and post-dive bubbles
Nico A.M. Schellart 1, Miroslav Rozložník 2, Costantino Balestra 2
1 Biomedical Engineering and Physics, Academic Medical Centre, University of Amsterdam,
Amsterdam, The Netherlands
2 Environmental and Occupational Physiology Laboratory, Haute Ecole ‘‘Paul Henri Spaak,’ Brussels, Belgium
Decompression sickness (DCS) in divers is caused by
bubbles of inert gas. When DCS occurs, most bubbles
can be found in the venous circulation: venous gas
emboli (VGE). Bubbles are thought to be stabilized by
low molecular weight surfactant reducing the plasma-air
surface tension (γ). Proteins may play a role as well. We
studied the interrelations between these substances, γ and
VGE, measured before and after a dry dive simulation.
VGE of 63 dive simulations (21-msw/40-minute pro-
le) of 52 divers was examined 40, 80, 120 and 160
minutes after surfacing (precordial Doppler method) and
albumin, total protein, triglycerides, total cholesterol and
free fatty acids were determined pre- and post-exposure.
To manipulate blood plasma composition, half of the
subjects obtained a fat-rich breakfast, while the other
half got a fat-poor breakfast pre-dive. Eleven subjects
obtained both. VGE scores measured with the precordial
Doppler method were transformed to the logarithm of
Kisman Integrated Severity Scores.
With statistical analysis, including (partial) correlations,
it could not be established whether γ as well as VGE scores
are related to albumin, total protein or total cholesterol.
With triglycerides and fatty acids correlations were also
lacking, despite the fact that these compounds varied sub-
stantially. The same holds true for the paired differences
between the two exposures of the 11 subjects. Moreover,
no correlation between surface tension and VGE could
be shown.
From these ndings and some theoretical consider-
ations it seems likely that proteins lower surface tension
rather than lipids. Since the ndings are not in con-
cordance with the classical surfactant hypothesis,
reconsideration seems necessary.
KEYWORDS: Diving, surface tension, surfactant, plasma lipids and
proteins, Doppler bubble score
Decompression sickness (DCS) is a disorder caused
by bubbles of inert gas (usually nitrogen; N2) after
surfacing. The large, potentially pathological bubbles
occur predominantly in the venous part of the circu-
lation (venous gas embolism; VGE [1,2]). They are
detectable by the precordial Doppler technique [3] or
by using echocardiography and counting circulating
bubbles in the ventricle [4].
VGE bubbles of divers, when exposed to the same
dive prole, show high variation. For many decades
the causes of this high variability remained largely un-
known. Recently various reports show that increasing
age stimulates VGE and DCS risk and a high VO2max
suppresses it ([5]). Some reports state that a severe patent
foramen ovale (PFO) and lung disorders are pre-
disposing, but there is not full agreement [6-8]. Other
demographic predisposing factors for VGE, such as
gender, are either unknown or in dispute. Recent
studies show that body fat (BF) and BMI are not
causally related with VGE but are clues since they
are correlated with age and VO2max [9,10].
VGE bubbles are thought to evolve from small nuclei
(101-103 nm in diameter) by heterogeneous nucleation
with several growth mechanisms hypothesized [11]
in facilitating regions: for instance favorable cavity
geometries [12], or from a self-regenerating popula-
tion of bubbles with short half-lives in elastic tissues
by the hypothetical mechanism of tribonucleation
[13,14]. For a discussion about the origin of nuclei
and microbubbles and their detachment from surfaces
N.A.M. Schellart, M. Rozložník , C. Balestra
the reader is referred to the respective literature (e.g.,
[12-16]) since this is beyond the aim of this study.
The large majority of the nuclei will collapse soon
after their genesis due to inward pressure exceeding
the bubble pressure. The excess inward pressure is
proportional to the bubble surface tension and in-
versely proportional with the bubble diameter. A small
minority grows into bubbles (>1 μm) and some will
develop into bubbles detectable by Doppler techniques.
There are a few generally accepted mechanisms or
conditions that accelerate bubble dissolution, such as
hydratation. A most effective one that is always “active”
is the oxygen window. Without this phenomenon, dis-
solution takes a considerably longer time and increases
DCS risk substantially [15].
In contrast, there are also mechanisms that slow
dissolution. One of the most discussed is the length-
ening of bubble life time by a surfactant [6,17]. Nuclei
and bubbles are, according to the classical surfactant
hypothesis, supposed to survive longer when they are
surrounded by a monomolecular layer of surfactant
molecules with low molecular weights [6,17]. Surfac-
tants by denition decrease surface tension, γ, in watery
liquids (for pure water at 20°C γ0 is 72.25 mN/m),
and hence also that of blood or plasma. This lowers
the inward pressure on the bubble, which is, in its most
elementary denition, 2(γ’−Г)/r + Pamb, where γ’ is
the surface tension without surfactant, Г the effect of
the surfactant and r bubble radius. The general
structure of a surfactant is a hydrophobic aliphatic
chain that ends with a polar group: for instance,
a carbonic acid salt (strongly polar) or an alcohol
(weakly polar). Sometimes they comprise more
than one chain, such as triglycerides or a more
complex hydrophilic head such as phospholipids. The
polar character of the dissolved substance should be in
some balance with its hydrophobicity to obtain a
substantial Г.
Adopting the hypothesis of the critical diameter
[19], this means that the critical diameter is reduced
by the surfactant layer. (Stable bubbles have diameters
greater than the critical diameter Dcrit. Below this
diameter bubbles will generally collapse.) As a conse-
quence with a surfactant, more bubbles will survive and
grow – ultimately into bubbles that can be detected.
In an animal study with a very severe dive prole
(20 msw/180 minutes; no decompression stops), it was
shown that after the simulation the plasma surface
tension was slightly (<1%) but signicantly diminished
by 0.4 mN/m. The pre-dive γ showed a negative cor-
relation with the number of bubbles. In other words,
a lower γ (meaning more surfactant) should favor
bubble formation, as is expected [20]. However, in a
recent human study with a 30-msw/30-minute sea
dive of eight military divers, γ was not related with
the grade of VGE [21]. The lack of agreement
between these two studies with signicantly different
designs proves new human studies very valuable.
The surface tension γ is assumed to be dependent on
many substances in the blood, especially on surfactants.
Anorganic ions hardly increase γ0. For comparison, sea
water (20°C) has a γ of 73.50 mN/m, only 1.25 mN/m
higher than pure water. In contrast, lipids, for in-
stance in detergents, substantially lower γ. The γ0
of the water-air interface can also be inuenced by
other factors, such as the concentration of the surfac-
tant, the temperature and the gas pressure. Individual
lipid molecules and their multimers do not oat to the
surface, as can be calculated with Stokes’ law. However,
once collected on the surface, they will stay there
and can form micelles, as happens with detergents.
It is not known which substances act as surfactants
in plasma [8,11,13]. In plasma, amphiphilic substances
(and so potential surfactants) are free fatty acids (FFA).
In a previous study a relationship between plasma free
fatty acids (FFAs) and VGE could not be established
[22]. Other surfactant candidates are plasma triglycerides
and cholesterol, both occurring in abundance. However,
they are not freely dissolved but bound to (lipo)proteins
and encapsulated in chylomicrons. The great majority
of triglycerides (TGl) are found in chylomicrons and
the remainder is bound in lipoproteins. The cholesterol
content of chylomicrons is about 10 times less than that
of TGl. Cholesterol is mainly bound in lipoproteins.
Both triglycerides and cholesterol will be examined for
their inuence on VGE and surface tension. In addition,
the surmised relationship between FFA and γ will be
Proteins reduce γ [23-26]. Therefore, plasma pro-
teins are of interest to study the γ-VGE relationship.
Albumin and lipoproteins transport non-dissolved
plasma lipids. With albumin, the lipids are bound to or
embedded in the protein. When bound, they are
predominantly located on the outside of the protein. At
the liquid-air interface, the hydrophobic aliphatic tails
point into the gas phase. In general, plasma proteins have
many lipid binding sites. With the lipoproteins, lipids are
located in the center of the protein and supposedly do not
N.A.M. Schellart, M. Rozložník , C. Balestra
affect the hydrophilicity. In a previous study, it was
found that plasma albumin does not correlate with
bubble grades, but its relationship with γ was not
examined [22].
From the above it is evident that insight into the
value of the γ is not trivial. Many substances and con-
ditions will play a role and it would be hard to unravel
the various effects. However, we must presume that γ
of microscopic gas bubbles in plasma is the same as
that of a macroscopic plasma-air interface, often the
condition of measurement.
By providing the subjects of this study with either
fat-rich or carbohydrate-rich meals preceding the dive
simulation, we tried to manipulate the lipid and
protein levels and consequently γ, which is expected to
result in a variation of bubble grades detectable with
the precordial Doppler technique [3].
The aim of the study is to re-examine whether γ
measured in plasma samples taken post-exposure is
negatively correlated with VGE bubbles. Furthermore,
it is hypothesized that γ (pre- and post-exposure) is
negatively correlated with albumin and total protein
due to their (quasi-) surfactantlike action. As a conse-
quence of this hypothesis, the hypothesis that VGE is
positively correlated with albumin and total protein
also needs testing.
Subjects and experimental study design
Experiments were performed in agreement with the
Declaration of Helsinki (2011) and Dutch law on
medical scientic research on humans (WHO, 2012;
certicate METC AMC 10/055). All subjects signed
an informed consent and were provided a written
The divers performed a simulated dive in air
(and breathing the ambient air) with an exposure to
21 meters of sea water (msw) for 40 minutes, a man-
datory ve-minute stop at 3 msw (according to the
DCIEM tables) and with a rate of compression and
decompression of 15 msw/minute [5].
A total of 52 non-smoking male subjects (both pro-
fessional and recreational divers) volunteered. They
were severely restricted to 40-50 years of age and a
VO2max of 35-52 ml, to preclude possible
multicollinearity effects of these predisposing factors
on the inuence of γ, lipids and proteins on VGE. All
subjects, after passing a medical examination were
not allowed to dive 48 hours prior to the dive simulation
(to avoid repetitive dive effects), nor were they to per-
form any endurance sports or heavy physical exercise
(which might diminish VGE). Additionally, they were
to abstain from using any recreational drugs for (at
least) one day prior to the examination. Further details
about inclusion criteria and methodology have been
described before [5].
The divers were divided into two matched groups.
The age, VO2max and percentage of body fat (Table 1)
of both groups were the same within 0.0-1.7%
(p-values of Student’s paired t-test 0.40, 0.84 and 0.90,
respectively). With a power of 0.80, a signicant dif-
ference of age, showing the largest relative difference
of the three, must be at least 2.6 years.
The night before the dive the rst group (FRi,
28 subjects) consumed a fat-rich diner at home and
a fat-rich simple continental breakfast at the test site,
provided 30 minutes pre-exposure. Similarly, the other
group (FPo, 24 subjects) consumed a fat-poor,
carbohydrate-rich dinner and breakfast.
To obtain standardized measurements the subjects
fasted the night before from 22:00. After awaking, at
least two hours pre-exposure, each consumed one glass
of water or pure weak tea. The breakfast contained
7 kcal per kg adjusted body weight [27], calculated
Table 1. Demographic information on the fat-rich meal group (FRi)
and the fat-poor meal group (FPo)
Group FRi, n=28 Group FPo, n=24*
Age VO2max body fat Age VO2max body fat
(years) (ml/kg.min) (%) (years) (ml/kg.min) (%)
mean 45.5 42.3 21.2 46.3 42.0 21.2
SD 3.47 4.82 2.9 3.10 6.62 4.2
*The difference in group size is caused by voluntary withdrawing of subjects.
136 N.A.M. Schellart, M. Rozložník , C. Balestra
from the ideal weight with the Devine equation [28].
The number of provided slices of bread (FRi with
cheese and butter, FPo with jam) were rounded to
half-slices and liquids to 25-ml units. The FRi subjects
received whole milk and the FPo subjects had apple
juice. The FRi breakfast comprised 35% carbohydrates,
41% fat and 24% protein; the FPo breakfast of 92%,
1% and 7% respectively, in weight percentage. Conse-
quently, the fatFRi/fatFPo ratio of the breakfast was 41.
After the rst Doppler session (post-exposure, see
below) the subjects received a body-weight-adjusted
glass of milk or apple juice respectively. Further
drinking and food were disallowed until after the last
Doppler session.
Eleven subjects performed the experiment both as
FRi as well as FPo volunteers.
After the simulation, a standardized interview
obtained information about food and liquid intake
(between 18:00 of the preceding day and the start of
breakfast) and adherence to the enrollment criteria.
Bubble grades were blindly determined precordially
at 40, 80, 120 and 160 minutes after surfacing (for
details see [5]). The recordings were, again blindly,
scored by a Doppler expert of the Defence Research
and Development Canada (DRDC), Toronto, Canada,
with the bubble grades expressed in Kisman-Masurel
(KM) units [3]. To allow parametric statistics, the
ordinal KM scores of 40, 80, 120 and 160 minutes
were transformed into a single numerical value, the
Kisman Integrated Severity Score (KISS) [29]. To en-
able parametric statistics, as far as possible and to
overcome the outlier problem, the logarithm of the
Kisman Integrated Severity Score (logKISS) was taken
Analyses of triglycerides (TGl), total cholesterol
(TCh), total protein (TPr), FFA (spectroscopic/colori-
metric method), albumin (colorimetric method) and γ
were determined from defrosted blood samples, taken
before breakfast and after the second Doppler deter-
mination (two hours 30 minutes after breakfast).
The FFA determination measures both FFA bound to
albumin as well as plasma dissolved FFA (dissolved
FFA being in the order of nM [22]).
Additionally, in the rst sample, gamma glutamyl
transpeptidase (GGT) was determined to verify the
subject abstained from the use (substantial) of
alcoholic drinks on the preceding day.
Surface tension was quantied using a SITA t60
Science Line tensiometer (SITA Messtechnic GmbH,
Dresden, Germany), which measures the dynamic sur-
face tension of uids in the range of 10–100 mN/m
and with a 0.1-mN/m resolution. Measurements were
performed at room temperature, nominally 20° C.
Differences between the actual temperature of the
sample (measured with the fast mini-thermocouple
probe GTH 1170, Greisinger Electronic GmbH,
Regenstauf, Germany), generally limited to less than
0.5° C, were used to correct the plasma γ according to
–0.15 mN.m-1.°C-1 (the γ-temperature dependency of
Statistical analysis
Pearson binary correlation coefcients (regular R and
partial ρ) and Spearman R were calculated. Control-
ling independent variables for ρ were grouped: TPr and
albumin and the lipids TCh, TGl and FFA. Normality
of the distributions was inspected with the KS-test.
p-values <0.05, tested double-sided (Student’s t test)
were considered signicant (α = 0.05). For sets of
p-values the Bonferroni-Holm (B-H) correction was
performed with α = p/(m+1–k), where m is the number
of variables tested and k the ranking number of their
uncorrected p-values from small to large. The number
m was reduced with the number of theoretical hypo-
theses as mentioned at the end of the Introduction.
Analyses were performed with SPSS 20.0. Occa-
sionally power (1–β) of the test was calculated.
During the night before and during the day of the
experiment, the subjects did fulll the requested con-
ditions and requirements for processing their data as
established by the interview after the simulation.
Signs and symptoms of DCS were neither observed
nor reported by the divers.
Raw KM values of the rst exposures and the KISS
values of all exposures can be found in previous studies
Group differences
In Table 2, the mean values of plasma substances, γ and
logKISS are presented. All distributions are normal,
except that of logKISS (KS-test). The parameters,
except logKISS, are given pre- and post-exposure
and for both the FRi as well as the FPo group.
With FRi, the differences post-pre are highly sig-
N.A.M. Schellart, M. Rozložník , C. Balestra
Table 2. Values of lipids FA, TGl and TCh, total protein (TPr) and albumin,
γ and logKISS of groups with fat-rich and fat-poor meals
Measured FAT-RICH GROUP (FRi), n=28 FAT-POOR GROUP (FPo), n=24 FRi - FPo
mean±SD mean± SD p-value pt test mean± SD mean±SD p-value pt test p-value t-test
FFA 0.37±0.15 0.20±0.08 5x10-7 0.54±0.21 0.078±0.049 1x10-10 7x10-8
TGl 1.46±1.12 2.04±2.02 7x10-5 1.49±1.05 1.41±0.96 0.064 0.03
TCh 5.68±1.1 5.58±1.1 0.29 5.68±1.1 5.58±1.1 0.029 0.92
albumin 46.4±2.4 46.6±2.7 0.77 47.1±2.6 47.5±2.0 0.31 0.15
TPr 71.8±4.1 71.5±4.7 0.69 71.4±3.7 71.8±2.9 0.47 0.81
γ 69.8±1.6 69.6±1.7 0.60 70.2±1.4 69.7±1.7 0.16 0.85
logKISS -0.61±1.50 -0.87±1.25 0.62+
Lipids in mM, albumin and TPr in g/L. 47 g albumin/L equals 0.70 mM. + KS-test. pt-test is paired t-test.
In bold italics, the significant p-values after B-H correction. All others are not significant.
Scatter diagram of γ1 versus TGl1.
Diamonds are FRi and squared FPo. The regression
is: γ1 = -0.90TGl1 +71.34 (R2 = 0.32).
gamma (mN/m)
0 1 2 3 4 5 6
triglycerides1 (mM)
Figure 1.
nicant for FFA and TGl (p<10-4). For FPo this
holds only for FFA. FFA also showed a large differ-
ence between the FRi and FPo group after simulation
(right column).
Correlations with surface tension
After B-H correction all correlations were not signicant
except Pearson’s R of γ1 (pre-exposure) with TGl1
Table 3. Partial correlations between γ and plasma
substances before (..1) and after (..2) breakfast and between
logKISS and plasma substances and γ2 after breakfast.
Dependent TCh1 TGl1 FFA1 alb1 TPr1
γ1 -.25 .24 -.10 -.19 .17
.060 .065 .45 .17 .21
Dependent TCh2 TGl2 FA2 alb2 TPr2 γ2
γ2 -.079 0.078 -.16 -.23 .31
.55 .56 .24 .09 .02*
logKISS .20 .20 .60 .92 .88 .93
Upper line in each row gives correlation coefficients and
lower lines the corresponding p-value. n=52.
* Not significant after B-H correction.
(R = –0.56, p=0.0003, as illustrated by Figure 1). How-
ever, using the partial correlation, the signicance
vanished due to the co-correlation with TCh. γ2
(post-exposure) correlated with TGl2 yielded near
signicance after B-H correction (p=0.019). TPr2 was
close to signicantly correlated with γ2 after B-H
correction (Table 3; α = 0.05/3).
Correlations with logKISS
Correlations (Spearman and γ) between logKISS and
any of the plasma substances were all (very) non-
signicant (B-H correction). With FRi and FPo,
none of the correlations (Spearman) of logKISS with
γ1 and γ2 for was signicant (B-H correction).
Multicollinearity with age, VO2max and BF was absent
(tested with partial correlations).
Within-subject FRi and FPo differences
With the 11 subjects who obtained both fat-rich and
fat-poor meals, paired t-tests were performed. After
the simulation, TGl and FFA were signicantly higher
with the FRi meal (both p=0.01). The post-pre differ-
ences of FRi and FPo with respect to FFA and TGl
conrm the ndings obtained with both subject groups
(Table 2). Post-exposure, γ of FPo tended to be 1.5
mN/m lower than pre-exposure (p=0.04, α = 0.05/2).
However, this post-pre difference was not signicant
for the FRi or for the FPo group (Table 2). None of the
pre-post differences of the plasma substances showed
a correlation with logKISS or with the γ pre-post differ-
ences. The FRi – FPo difference of TGl1 correlated
negatively with the FRi FPo difference of γ1
(p=0.01; α = 0.05/3).All analyses were also performed
on those subjects who were positive for Doppler
bubbles (KISS>0). However, the results also showed
no consistent effects on γ and VGE.
The main aim of this study was to establish the rela-
tionship between bubble grade, surface tension γ and
plasma substances. Analyses of the 52 dive simulations
(rst exposures) and of the 11 paired simulations
showed no consistent correlations of pre- and post-
exposure between plasma substances and γ (Tables 2
and 3). Also no relationship between logKISS and any
variable, including γ was found. This study conrms
our ndings in an earlier study of the γ-VGE relation-
ship with eight military divers as subjects [21].
Plasma compounds as potential surfactant revisited
One can wonder why all the investigated substances
surprisingly showed no consistent association with γ.
Surfactant concentration lowers surface tension roughly
linearly, with a saturating effect at high concentra-
tions [30]. Therefore, the SD/mean ratio of the sub-
stance is a leading variable to evaluate possible effects.
The TGl concentration varies substantially among
subjects (SD/m≈0.8). However, the negative associa-
tion between surface tension and TGl before exposure,
shown in Figure 1, appeared not to be reproducible.
(Multicollinearity with lipids and proteins was observed
pre-exposure and also multicollinearity with unknown
substances or mechanisms may have played a role.)
FFAs are freely dissolved in nM concentrations, too
little to inuence surface tension [30]. Nearly all FFAs
are bound to proteins, especially to albumin. The total
area that can be covered by FFA-albumin is many
orders of magnitude higher than the total surface of all
(micro) bubbles [22]. FFAs vary substantially between
subjects and between meal types (SD/m≈0.5). The
polarity of albumin is increased slightly by binding
FFA, but probably not enough to change the albumin
effect on γ substantially. Therefore, with respect to γ,
the total albumin concentration is far more important
than FFA-albumin. In contrast, the total albumin con-
centration is relatively constant (SD/m≈0.05). Thus
the concentration effect on γ is expected to be very
small, as in fact it is irrelevant and not demonstrable.
The same holds for the total plasma protein content.
TCh is bound to lipoproteins and hardly affects the
polarity of the complex. Moreover, it varies only slightly
among subjects (SD/m≈0.20). Again, the effect will
be negligible.
The above sheds some light on the observation that
effects were not shown (except the γ1-TGl1 univariate
regression). But there are possibly additional causes.
Therefore, some disputable aspects of the study design
will be discussed before entering into a discussion of
the chemical nature of the surfactant layer.
Disputable and strong points
Since all subjects passed the medical examination one
might think that lipid values were within the normal
values. Surprisingly, nearly half of the individual values
were above the norm, though not pathological. This
enhanced the high SD/m ratios.
Surface tension determinations of plasma or blood
are dependent on the technique used. Any one method
shows a bias when compared to another. For the cor-
relation coefcients and comparisons between groups
this is deemed to be irrelevant, but when actual
values are needed the bias must be estimated.
In the last two decades studies showed a range
in blood and plasma γ values from 55.9 to 73.5
[20,21,31,32]. The dynamic bubble method, used here
N.A.M. Schellart, M. Rozložník , C. Balestra
consistently, gives an overestimate, which becomes
asymptotically smaller with bubble life time in the
sample barrel. From data in literature [30] it can be
derived that the overestimation is about 13 mN/m,
yielding 57 mN/m after correction for the bubble life
time. Consequently, the reduction of γ0 by the plasma
compounds is 15 mN/m only. The estimated value of
57 mN/m is close to the average value of 59.9 mN/m
obtained by static γ methods used on plasma or
blood [20,31,32].
Since uid intake was controlled, it is supposed that
blood-volumetrically the subjects are comparable. This
then should not be a factor inuencing γ. Moreover,
a 10% change in the blood volume will not change γ
for more than 1 mN/m, as can be estimated from data
about the effect of the concentration on γ [26,30].
The design of the 63 simulations, including the 11
paired simulations, is an optimized approach within
the constraints of the limited availability of subjects.
Although in the eld of diving physiology these test
numbers are not small, they certainly make it difcult
to resolve small effects. TPr and albumin showed a
maximum/minimum ratio of about a factor 1.35, TCh of
3.0, TGl of 13 and FFA of 45. The lack of signicance
suggests that if effects do exist they would be small.
Intra-subject differences showed smaller SD/mean
ratios than the FRi-FPo differences of all subjects.
In other words, the intra-subject differences are less
noisy. Despite this, with the 11 subjects exposed twice
none of the substances showed a signicant relation-
ship with logKISS or γ.
What substances form the bubble skin?
In a previous study, it was argued that the level of dis-
solved monomolecular long-chain fatty acids as poten-
tial surfactant is much too low (nM) to form surfactant
monolayers since the critical micelle concentration is
several orders of magnitude higher (mM) [22]. This is
in accordance with the experimental ndings that the
albumin-bound FFA and the dissolved FFA showed no
relationship with VGE (this study and [22]).
Triglycerides lacked any association with γ and VGE.
Theoretically this is not surprisingly, since these alcohol-
esters are but weakly polar and their 3D structure
seems to be inappropriate to form regular monolayers.
Moreover, long-chain triglycerides, by far the most
numerous, are insoluble. Similar considerations hold
for the highly heterogeneous class of phospholipids
with very low to no solubility and a 3D structure
unlikely to form spontaneously regular monolayers.
It is noted that in the alveoli, the construction of the
surfactant layer is a biochemical process and more-
over it is probably not a single- but a multimonolayer.
The third plasma lipid, cholesterol, a sterol, has
a poor water solubility (0.25 µM at 30° C). Yet, it
occurs in ample quantity to form monolayers on all
nuclei and bubbles (for a calculation see [22]). It is
barely amphiphilic since its OH group is only weakly
polar and its 3-D structure is not well suited to form
regular monolayers. In addition to the three mentioned
lipids, plasma also contains many small lipid fractions
with shorter FA-chains. They cannot be ruled out as
surfactant candidates since they are much more soluble
and occur perhaps in small but sufcient quantities.
One example is the shortest medium-chain FFA,
octanoic acid (C8) and another the medium-chain
triglycerides. However, their effect will be progressively
smaller due to their shorter chains.
Dening the bubble-stabilizing effect as Г/γ0 this
gives 21% (=15/72.25). Assuming the correctness of the
hypothesis of the critical diameter [19], this diameter
is also diminished by 21%. Possibly, this is too small
to affect VGE (the underlying bubble numbers of the
KM scale show a nearly logarithmic relation with the
KM grades [3]). In comparison, water with detergent-
containing fatty acids lowers the surface tension
approximately 35 mN/m, being a decrease of about
50%. This might be enough to be just detectable.
Also, protein solutions, such as dissolved albumins
lower the surface tension [23-25,33]. Different types
of milk (skim and whole) have a γ’ close to 50 mN/m.
The possible reason why whole milk (fresh) and skim-
med milk have about the same γ is that the lipids in
whole milk occur as microscopic fat-droplets. These
droplets cannot contribute well to a surfactant bubble
skin and hence hardly change bubble surface tension.
Proteins, especially albumin, are the substances low-
ering surface tension of milk. Indeed, it has been
found that albumin can stabilize bubbles [26]. The
amount of albumin (ca. 0.70 mM; molecule diameter
15 nm) is many orders of magnitude larger than is
needed to cover all gas nuclei and bubbles with a
monolayer [22]. Therefore it cannot modulate VGE.
Since the albumin level is practically the same in all
subjects it also will not modulate γ in a detectable way.
Despite the results of this study it is not certain that
the venous bubbles, here measured with the precordial
Doppler technique, lack a classical surfactant and are
N.A.M. Schellart, M. Rozložník , C. Balestra
1. Eftedal OS, Lydersen S, Brubakk AO. The relationship
between venous gas bubbles and adverse effects of decom-
pression after air dives. Undersea Hyperbaric Med 2007;
2. Vann RD, Butler FK, Mitchell SJ, Moon RE.
Decompression illness, Review. Lancet. 377;153-164:2011
3. Nishi RY, Brubakk AO, Eftedal OS. Bubble detection.
In: Brubakk AO and Neuman TS (ed) Bennett and Elliott’s
Physiology and medicine of diving. London: WB Saunders,
4. Germonpré P, Papadopoulou V, Hemelryck W, Obeid G,
Lafere P, Eckersley RJ, Tang MX, Balestra C. The use of
portable 2D echocardiography and ‘frame-based’ bubble
counting as a tool to evaluate diving decompression stress.
Diving Hyperb Med. 2014; 44:5-13.
5. Schellart NA, van Rees Vellinga TP, van Hulst RA.
Body fat does not affect venous bubble formation after air
dives of moderate severity: theory and experiment. J Appl
Physiol 2013; 114:602-610.
6. Saary MJ, Gray GW. A review of the relationship
between patent foramen ovale and type II decompression
sickness. Aviat Space Environ Med. 2001; 72:1113-1120.
7. Blogg SL, Gennser M, Møllerløkken A, Brubakk AO.
Ultrasound detection of vascular decompression bubbles: the
inuence of new technology and considerations on bubble
load. Diving Hyperbaric Med. 2014; 44:35-44. Review.
8. Parlak IB, Egi SM, Ademoglu A, et al. Bubble stream
reveals Functionality of the right-to-left shunt: detection of
a potential source for air embolism. Ultrasound Med & Biol
2014; 40:330-340.
9. Carturan D, Boussuges A, Vanuxem P, Bar-Hen A,
Burnet H, Gardette B. Ascent rate, age, maximal oxygen
uptake, adiposity, and circulating venous bubbles after diving.
J Appl Physiol 2002; 93:1349-1356.
10. Schellart NAM, van Rees Vellinga TP, van Dijk FH,
Sterk W. Doppler bubble grades after diving and relevance
of body fat. Aviat Space Environ Med 2012; 83: 951-957
covered by a protein layer, since this can be established
only by a direct visualization with submicroscopic tech-
niques. In the literature it is speculated that platelets
contact freely moving bubbles with articial surfactants,
resulting in platelet activation and logging of the bubble-
platelet structures (e.g., [34]). However, also without
articial surfactant, platelets are assumed to be activated
by vascular bubbles in divers [35]. When coated with
a protein layer of albumin or other proteins, platelet-
bubble interaction may be different since the surface
tensions are higher (some 20 mN/m) than in the study
with the articial surfactants. We can then assume that
the molecular interactions (platelet-protein skin) will be
different, too. This is thought to trigger a multi-
cascade of hematological processes leading to DCS
(NO-metabolism, free oxygen radicals, etc.). However,
their description is beyond the scope and aim of this
The experimental results do not show signicant and
consistent effects of plasma lipids and proteins on sur-
face tension. The surface tension of plasma is higher
than expected, and plasma seems to contain insuf-
cient effective lipid surfactants to lower bubble surface
tension. The plasma substances do not affect VGE.
Moreover, VGE bubbles do not correlate with surface
tension, although a limited role of short-chain lipids
cannot be excluded totally. The plasma surface tension
is estimated to be approximately 15 mN/m lower than
that of water. Possibly, this decrease is caused by a
mixture consisting predominantly of proteins, such
as albumin, surrounding the bubbles. Lipids probably
play a minor role or do not contribute. Consequently,
the classical surfactant hypothesis seems not directly
applicable in complex physiological uids in vivo,
and one may ask whether the hypothesis is ready for
The authors would like to thank Dr. R. van Hulst for
providing the hyperbaric chamber and other technical
facilities of the Dive Medical Centre, Dutch Royal Navy,
Den Helder, Tjeerd van Rees Vellinga, M.D., for performing
the Doppler recordings, Jan van Straaten for the chemical
analyses, and the Nederlandse Vereniging voor Duikgenee-
skunde (NVD) for a grant to have the chemical analyses
performed. Finally, the authors thank all the subjects who
participated in this study. For MR this study is part of the
Phypode Project FP7 (grant no. 264816) under a Marie
Curie Initial Training Network program.
Conict of interest
The authors have declared that no conict of interest exists
with this submission. n
140 N.A.M. Schellart, M. Rozložník , C. Balestra
N.A.M. Schellart, M. Rozložník , C. Balestra
11. Papadopoulou V, Eckersley RJ, Balestra C, Karapantsios
TD, Tang MX. A critical review of physiological bubble
formation in hyperbaric decompression. Adv Colloid
Interface Sci. 2013; 191-192:22-30. Review.
12. Chappell MA, Payne SJ. A physiological model of the
interaction between tissue bubbles and the formation of
blood-borne bubbles under decompression. Phys Med Biol.
2006; 51:2321-2338
13. Goldman S. Free energy wells for small gas bubbles in
soft deformable materials. J Chem Phys. 2010; 132:164509.
14. Vann RD. Mechanisms and risks of decompression.
In: Bove AA, ed. Bove and Davis’ Diving Medicine, 4th ed.
Philadelphia: Saunders; 2004:127-164
15. Vann RD. Inert gas exchange and bubbles. In: Bove AA,
ed. Bove and Davis’ Diving Medicine. 4th ed. WB Philadel-
phia: Saunders; 2004:53-76.
16. Papadopoulou V, Tang MX, Balestra C, Eckersley RJ,
Karapantsios TD. Circulatory bubble dynamics: from
physical to biological aspects. Adv Colloid Interface Sci.
17. Yount DE, Kunkle TD, D’Arrigo JS, et al. Stabilization
of gas cavitation nuclei by surface-active compounds. Aviat
Space Environ Med 1977; 48:185-191
18. Blatteau JE, Souraud JB, Gempp E, Boussuges A.
Gas nuclei, their origin, and their role in bubble formation.
Aviat Space Environ Med. 2006; 77:1068-1076.
19. Van Liew HD, Raychaudhuri S. Stabilized bubbles in
the body: pressure-radius relationships and the limits to
stabilization. J. Appl. Physiol 1997; 82:2045-2053.
20. Hjelde A, Brubakk AO. Variability in serum surface
tension in man. Appl Cardiopulm Pathophysiol 2000;9:9-12.
21. Gempp E, Blatteau J E, Pontier JM, Balestra C, Louge P.
Preventive effect of pre-dive hydration on bubble formation
in divers Br J Sports Med 2009; 43:224-228.
22. Schellart NAM. Free fatty acids do not inuence
venous gas embolism in divers. Aviat Space Environ Med.
23. Camejo G, Colacicco G, Rapport MM. Lipid monolayers:
interactions with the apoprotein of high density plasma lipo-
protein. J Lipid Res 1968; 9:562-569.
24. Absolom DR, Van Oss CJ, Zingg W, Neumann AW.
Determination of the surface tension of proteins. I. Surface
tension of native serum proteins in aqueous media. Biochim
Biophys Acta 1981; 670:64-73.
25. Wang L, Walsh MT, Small DM. Apolipoprotein B is
conformationally exible but anchored at a triolein-water
interface: A possible model for lipoprotein surfaces. Proceed
Nat Acad Science, 2006; 103:6871-6876.
26. Eckmann DM, Zhang J. Gas embolism and Surfactant-
based intervention implications for long-duration space-
based activity. Ann. NY Acad Sci 2006; 1077:256–269 ().
27. Mittendorfer B, Magkos F, Fabbrini E, Mohammed BS,
Klein S. Relationship between body fat mass and free fatty
acid kinetics in men and women. Obesity 2009; 17:1872-1877.
28. Pai MP, Paloucek FP. The origin of the “ideal” body
weight equations. Ann Pharmacother. 2000; 34:1066-1069.
29. Jankowski LW, Nishi RY, Eaton DJ, Grifn AP. Exercise
during decompression reduces the amount of venous gas
emboli. Undersea Hyperbaric Med 1997: 24:59-65.
30. Christov NC, Danov KD, Kralchevsky PA, Ananthapad-
manabhan KP, Lips A. Maximum bubble pressure method:
universal surface age and transport mechanisms in surfactant
solutions. Langmuir. 2006; 22:7528-7542.
31. Rosina J, Kvasnák E, Suta D, Kolárová H, Málek J,
Krajci L. Temperature dependence of blood surface tension.
Physiol Res. 2007; 56:S93-98.
32. Hrncír E, Rosina J. Surface tension of blood. Physiol
Res. 1997; 46:319-321.
33. Suttiprasit P, Krisdhasima V, McGuire J. The surface
activity of α-lactalbumin, β-lactoglobulin, and bovine serum
albumin. I. Surface tension measurements with single-
component and mixed solutions. J Colloid Interface Science,
1992; 154:316-326.
34. Eckmann DM, Armstead SC, Mardini F. Surfactants
reduce platelet-bubble and platelet-platelet binding induced
by in vitro air embolism. Anesthesiology. 2005; 103:1204-
35. Olszański R, Radziwon P, Piszcz J, Jarzemowski J,
Gosk P, Bujno M, Schenk JF. Activation of platelets and
brinolysis induced by saturated air dives. Aviat Space
Environ Med. 2010; 81:585-858.
... Therefore, in order to determine the eff ect of a certain preconditioning procedure, it is of paramount importance that not only the dive profi le, but also the diver biometrics be standardized as much as possible; moreover, the diving experience, exercise, smoking, and possibly even dietary habits should also also be controlled as much as possible. 32 Th ere appears to be a potentially large difference in VGE postdive for a similar pressure-nitrogen exposure, depending on whether the dive was performed " wet " or " dry. " 24 Th e presumed micronuclei-originated VGE production is consistent with the fact that a certain form of " acclimatization " to decompression stress seems to exist, with a higher probability of VGE for the fi rst dives aft er a period of nondiving. ...
Full-text available
Background: Using ultrasound imaging, vascular gas emboli (VGE) are observed after asymptomatic scuba dives and are considered a key element in the potential development of decompression sickness (DCS). Diving is also accompanied with vascular dysfunction, as measured by flow-mediated dilation (FMD). Previous studies showed significant intersubject variability to VGE for the same diving exposure and demonstrated that VGE can be reduced with even a single pre-dive intervention. Several preconditioning methods have been reported recently, seemingly acting either on VGE quantity or on endothelial inflammatory markers. Methods: Nine male divers who consistently showed VGE postdive performed a standardized deep pool dive (33 m/108 ft, 20 min in 33°C water temperature) to investigate the effect of three different preconditioning interventions: heat exposure (a 30-min session of dry infrared sauna), whole-body vibration (a 30-min session on a vibration mattress), and dark chocolate ingestion (30 g of chocolate containing 86% cocoa). Dives were made one day per week and interventions were administered in a randomized order. Results: These interventions were shown to selectively reduce VGE, FMD, or both compared to control dives. Vibration had an effect on VGE (39.54%, SEM 16.3%) but not on FMD postdive. Sauna had effects on both parameters (VGE: 26.64%, SEM 10.4%; FMD: 102.7%, SEM 2.1%), whereas chocolate only improved FMD (102.5%, SEM 1.7%). Discussion: This experiment, which had the same subjects perform all control and preconditioning dives in wet but completely standardized diving conditions, demonstrates that endothelial dysfunction appears to not be solely related to VGE.Germonpré P, Balestra C. Preconditioning to reduce decompression stress in scuba divers. Aerosp Med Hum Perform. 2017; 88(2):114-120.
... Circulating bubbles can act on the endothelial lining of vessels directly or via increased shear stress, resulting in perturbations, activation or even stripping of endothelial cells 25 . As with foreign material, bubbles can initiate biochemical cascades including activation of coagulation, platelet aggregation, inflammatory responses, and lead ultimately to endothelial damage 13,33 . No matter how bubbles injure endothelia, the indices measured in this study herald endothelial activation and dysfunction, and are sensitive markers of decompression stress, especially for the assessment of divers with subclinical manifestations. ...
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Previous studies have documented that decompression led to endothelial dysfunction with controversial results. This study aimed to clarify the relationship between endothelial dysfunction, bubble formation and decompression rate. Rats were subjected to simulated air dives with one of four decompression rates: one slow and three rapid. Bubble formation was detected ultrasonically following decompression for two hours, before measurement of endothelial related indices. Bubbles were found in only rapid-decompressed rats and the amount correlated with decompression rate with significant variability. Serum levels of ET-1, 6-keto-PGF1α, ICAM-1, VCAM-1 and MDA, lung Wet/Dry weight ratio and histological score increased, serum NO decreased following rapid decompression. Endothelial-dependent vasodilatation to Ach was reduced in pulmonary artery rings among rapid-decompressed rats. Near all the above changes correlated significantly with bubble amounts. The results suggest that bubbles may be the causative agent of decompression–induced endothelial damage and bubble amount is of clinical significance in assessing decompression stress. Furthermore, serum levels of ET-1 and MDA may serve as sensitive biomarkers with the capacity to indicate endothelial dysfunction and decompression stress following dives.
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Diving often causes the formation of 'silent' bubbles upon decompression. If the bubble load is high, then the risk of decompression sickness (DCS) and the number of bubbles that could cross to the arterial circulation via a pulmonary shunt or patent foramen ovale increase. Bubbles can be monitored aurally, with Doppler ultrasound, or visually, with two dimensional (2D) ultrasound imaging. Doppler grades and imaging grades can be compared with good agreement. Early 2D imaging units did not provide such comprehensive observations as Doppler, but advances in technology have allowed development of improved, portable, relatively inexpensive units. Most now employ harmonic technology; it was suggested that this could allow previously undetectable bubbles to be observed. This paper provides a review of current methods of bubble measurement and how new technology may be changing our perceptions of the potential relationship of these measurements to decompression illness. Secondly, 69 paired ultrasound images were made using conventional 2D ultrasound imaging and harmonic imaging. Images were graded on the Eftedal-Brubakk (EB) scale and the percentage agreement of the images calculated. The distribution of mismatched grades was analysed. Fifty-four of the 69 paired images had matching grades. There was no significant difference in the distribution of high or low EB grades for the mismatched pairs. Given the good level of agreement between pairs observed, it seems unlikely that harmonic technology is responsible for any perceived increase in observed bubble loads, but it is probable that our increasing use of 2D ultrasound to assess dive profiles is changing our perception of 'normal' venous and arterial bubble loads. Methods to accurately investigate the load and size of bubbles developed will be helpful in the future in determining DCS risk.
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'Decompression stress' is commonly evaluated by scoring circulating bubble numbers post dive using Doppler or cardiac echography. This information may be used to develop safer decompression algorithms, assuming that the lower the numbers of venous gas emboli (VGE) observed post dive, the lower the statistical risk of decompression sickness (DCS). Current echocardiographic evaluation of VGE, using the Eftedal and Brubakk method, has some disadvantages as it is less well suited for large-scale evaluation of recreational diving profiles. We propose and validate a new 'frame-based' VGE-counting method which offers a continuous scale of measurement. Nine 'raters' of varying familiarity with echocardiography were asked to grade 20 echocardiograph recordings using both the Eftedal and Brubakk grading and the new 'frame-based' counting method. They were also asked to count the number of bubbles in 50 still-frame images, some of which were randomly repeated. A Wilcoxon Spearman ρ calculation was used to assess test-retest reliability of each rater for the repeated still frames. For the video images, weighted kappa statistics, with linear and quadratic weightings, were calculated to measure agreement between raters for the Eftedal and Brubakk method. Bland-Altman plots and intra-class correlation coefficients were used to measure agreement between raters for the frame-based counting method. Frame-based counting showed a better inter-rater agreement than the Eftedal and Brubakk grading, even with relatively inexperienced assessors, and has good intra- and inter-rater reliability. Frame-based bubble counting could be used to evaluate post-dive decompression stress, and offers possibilities for computer-automated algorithms to allow near-real-time counting.
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Bubbles can form in the body during or after decompression from pressure exposures such as those undergone by scuba divers, astronauts, caisson and tunnel workers. Bubble growth and detachment physics then becomes significant in predicting and controlling the probability of these bubbles causing mechanical problems by blocking vessels or displacing tissues, or inducing an inflammatory cascade if they persist for too long in the body before being dissolved. By contrast to decompression induced bubbles whose site of initial formation and exact composition are debated, there are other instances of bubbles in the bloodstream which are well defined. Gas emboli unwillingly introduced during surgical procedures and ultrasound microbubbles injected for use as contrast or drug delivery agents are therefore also discussed. After presenting the different ways bubbles can end up in the human bloodstream, the general mathematical formalism related to the physics of bubbles growth and detachment from decompression is reviewed. Bubble behavior in the bloodstream is then discussed, including bubble dissolution in blood, bubble rheology and biological interactions for the different cases of bubble and blood composition considered.
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To provide a historical perspective on the origin and similarity of the "ideal" body weight (IBW) equations, and clarify the terms ideal and lean body weight (LBW). Primary and review literature were identified using MEDLINE (1966-November 1999) and International Pharmaceutical Abstracts (1970-November 1999) pertaining to ideal and lean weight, height-weight tables, and obesity. In addition, textbooks and relevant reference lists were reviewed. All articles identified through the data sources were evaluated. Information deemed to be relevant to the objectives of the review were included. Height-weight tables were generated to provide a means of comparing a population with respect to their relative weight. The weight data were found to correlate with mortality and resulted in the use of the terms desirable or ideal to describe these weights. Over the years, IBW was interpreted to represent a "fat-free" weight and thus was used as a surrogate for LBW. In addition, the pharmacokinetics of certain drugs were found to correlate with IBW and resulted in the use of IBW equations published by Devine. These equations were consistent with an old rule that was developed from height-weight tables to estimate IBW. Efforts to improve the IBW equations through regression analyses of height-weight data resulted in equations similar to those published by Devine. The similarity between the IBW equations was a result of the general agreement among the various height-weight tables from which they were derived. Therefore, any one of these equations may be used to estimate IBW.
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Abstract: The surface tension of blood may play a role in intravascular bubble formation after decompression. This study involves surface tension in serum derived from two different populations; 25 individuals (group A) and 29 individuals with a high lipid level in blood (group B). The surface tension was measured at 21 - 23 degrees C with a drop-volume method. The mean surface tension in 25 healthy individuals was 68.8 +/- 0.70 dynes/cm. A significant intraindividual variation (1.11 +/- 0.73%) was observed in surface tension over a period of 6 months. The effect of freezing the serum samples resulted in a mean decline in surface tension of 2.2 +/- 0.8 dynes/cm, which was significant. The surface tension in the individuals with a high blood lipid level was 63.8 +/- 1.6 dynes/cm, which is significantly lower than that of the normal group. We conclude that serum surface tension varies over time within each individual. The effect of freezing and storing the samples had a significant impact on surface tension. High lipid level in serum causes a lower surface tension compared to normal serum.
Background: Decompression sickness is caused by bubbles of inert gas predominantly found in the venous circulation. Bubbles may exist longer when covered by a surfactant layer reducing surface tension. Surfactant candidates, based on 3D-structure and availability, are long-chain fatty acids (FFAs). It is hypothesized that sufficient molecular dissolved FFA (dFFA) result in higher bubble grades (BGs). Methods: Participating divers (52) either had a fat-rich or a fat-poor breakfast. After a dry dive simulation (21 msw/40 min), BGs were determined at 40, 80, 120, and 160 min after surfacing by the precordial Doppler method. The four individual scores were transformed to the Kisman Integrated Severity Score (KISS). Results: Kiss was not affected by meal fat content, and KISS and dFFA (calculated) were not associated, even though the fat-rich group had 3.5 times more dFFA. A paired approach (11 subjects exposed to fat-rich and fat-poor meals) yielded the same results. The measured FFA (albumin bound) was present in abundance, yet the long-chain dFFA concentration was probably too low (nM range) to form a surfactant monolayer, as follows from micelle theory. Conclusion: Bubble scores are not associated with dFFAs. Theoretically it is questionable whether long-chain dFFAs could form post-dive monolayers. It remains unclear which substance forms the surfactant layer around bubbles.
The existence of a right-to-left shunt may increase the likelihood of micro-embolism by allowing a flux of bubbles under hyperbaric conditions. The aim of the study was to measure the relationship between these shunts and bubbles in 10 consecutive subjects using trans-thoracic and trans-esophageal echocardiography. In video frames, all cardiac chambers were segmented and bubbles were analyzed by our proposed method and two other methods. The relationship with bubbles and shunts was divided into three classes: no bubbles, 1-20 bubbles, >20 bubbles and measured over 2160 frames. Our sensitivity was 100% and our specificity was between 90.1% and 96.4%. There were 4.32-23.78 bubbles/frame in the left atrium according to our method. After the automatic analysis, shunts were graded double-blinded by two cardiologists. Consequently, we noted that aperture size does not necessarily reflect how active the right-to-left shunt is. Instead, our proposed decay curves constitute a better tool for determining functionality.