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fphys-10-00807 July 10, 2019 Time: 17:14 # 1
HYPOTHESIS AND THEORY
published: 11 July 2019
doi: 10.3389/fphys.2019.00807
Edited by:
Richard D. Boyle,
National Aeronautics and Space
Administration (NASA), United States
Reviewed by:
Danilo Cialoni,
Dan Europe Foundation, Italy
Jacek Kot,
Medical University of Gda ´
nsk, Poland
Rodrigue Pignel,
Université de Genève, Switzerland
*Correspondence:
Salih Murat Egi
smegi@daneurope.org
Specialty section:
This article was submitted to
Environmental, Aviation and Space
Physiology,
a section of the journal
Frontiers in Physiology
Received: 03 February 2019
Accepted: 06 June 2019
Published: 11 July 2019
Citation:
Imbert J-P, Egi SM, Germonpré P
and Balestra C (2019) Static
Metabolic Bubbles as Precursors
of Vascular Gas Emboli During Divers’
Decompression: A Hypothesis
Explaining Bubbling Variability.
Front. Physiol. 10:807.
doi: 10.3389/fphys.2019.00807
Static Metabolic Bubbles as
Precursors of Vascular Gas Emboli
During Divers’ Decompression: A
Hypothesis Explaining Bubbling
Variability
Jean-Pierre Imbert1, Salih Murat Egi2,3*, Peter Germonpré3,4 and Costantino Balestra3,5
1Divetech, Biot, France, 2Department of Computer Engineering, Galatasaray University, Istanbul, Turkey, 3DAN Europe
Research Division, Divers Alert Network (DAN), Roseto, Italy, 4Centre for Hyperbaric Oxygen Therapy, Military Hospital
Brussels, Brussels, Belgium, 5Environmental, Occupational and Ageing Physiology Laboratory, Haute Ecole
Bruxelles-Brabant (HE2B), Brussels, Belgium
Introduction: The risk for decompression sickness (DCS) after hyperbaric exposures
(such as SCUBA diving) has been linked to the presence and quantity of vascular
gas emboli (VGE) after surfacing from the dive. These VGE can be semi-quantified
by ultrasound Doppler and quantified via precordial echocardiography. However, for
an identical dive, VGE monitoring of divers shows variations related to individual
susceptibility, and, for a same diver, dive-to-dive variations which may be influenced
by pre-dive pre-conditioning. These variations are not explained by currently used
algorithms. In this paper, we present a new hypothesis: individual metabolic processes,
through the oxygen window (OW) or Inherent Unsaturation of tissues, modulate the
presence and volume of static metabolic bubbles (SMB) that in turn act as precursors
of circulating VGE after a dive.
Methods: We derive a coherent system of assumptions to describe static gas bubbles,
located on the vessel endothelium at hydrophobic sites, that would be activated during
decompression and become the source of VGE. We first refer to the OW and show that
it creates a local tissue unsaturation that can generate and stabilize static gas phases
in the diver at the surface. We then use Non-extensive thermodynamics to derive an
equilibrium equation that avoids any geometrical description. The final equation links the
SMB volume directly to the metabolism.
Results and Discussion: Our model introduces a stable population of small gas
pockets of an intermediate size between the nanobubbles nucleating on the active
sites and the VGE detected in the venous blood. The resulting equation, when checked
against our own previously published data and the relevant scientific literature, supports
both individual variation and the induced differences observed in pre-conditioning
experiments. It also explains the variability in VGE counts based on age, fitness, type
and frequency of physical activities. Finally, it fits into the general scheme of the arterial
bubble assumption for the description of the DCS risk.
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Imbert et al. Static Metabolic Bubbles in Divers
Conclusion: Metabolism characterization of the pre-dive SMB population opens
new possibilities for decompression algorithms by considering the diver’s individual
susceptibility and recent history (life style, exercise) to predict the level of VGE during
and after decompression.
Keywords: diving, decompression sickness, desaturation, oxygen window, pre-conditioning
INTRODUCTION
Hyperbaric exposures such as SCUBA diving are associated with a
risk of decompression sickness (DCS). Traditionally, this risk has
been attributed to the presence and quantity of decompression
bubbles in the blood (vascular gas emboli or VGE) causing blood
flow occlusion in various tissues. Recently, DCS has also been
associated to the presence of blood microparticles and some
symptoms linked to an inflammatory process (Thom et al., 2011;
Arieli et al., 2015;Spisni et al., 2017).
In order to limit the risk of DCS, decompression procedures
have been developed, as early as from 1908 (Haldane’s first
experiments and publication of “dive decompression tables”).
Although most diving operations are still conducted with
empirical models, there has been a continuous research for
editing safer decompression tables based on more realistic
algorithms (Hugon, 2014). Various models have been developed
and tested, and some have been implemented in diving
decompression computers like the Bühlmann ZHL16 algorithm.
The objective of these models is to avoid or reduce
bubble formation. However, there is evidence that bubbles are
present in most, if not all decompressions, without necessarily
representing a threat for the diver (Papadopoulou et al.,
2013, 2015). VGE have been detected during decompression
by trans-thoracic ultrasonic Doppler since 35 years. These
bubbles have been estimated to be of 50 µm or larger
size, in order to be detectable (Spencer, 1976). Graded levels
of bubble detection have been used as an indication of
decompression stress and, indirectly, risk of DCS (Nishi et al.,
2003). A more sensitive method of monitoring is based on
2D echocardiography and uses actual bubble counts as an
indication of the decompression stress (Germonpre et al., 2014).
However, the resolution of the standard B-mode echography
technique remains limited to roughly 35 µm (Papadopoulou
et al., 2014, 2017), and it is reasonable to accept that in many
divers, undetectable smaller precursor bubbles are present. The
variability observed in levels of VGE measured in different divers,
even when performing exactly the same dive profile, suggests
that these precursors play an essential role in VGE production
(Papadopoulou et al., 2018).
While current technology does not allow the direct detection
of the precursors of these large vascular (venous) bubbles, their
existence has been proven by indirect experiments in shrimps
(Evans and Walder, 1969) and rats (Vann et al., 1980). These
precursors were named “gas micronuclei” and estimated to
be the size of 50–100 nm (Arieli et al., 2002). Linking these
micronuclei to actual VGE detected in decompressing divers is
still a matter of debate and requires several steps (Blatteau et al.,
2006;Doolette, 2019).
The first step deals with cavitation in physical systems. Hills
showed that cavitation occurs at the liquid/liquid interface after
decompression when one of the liquids is hydrophobic (Hills,
1967). Recently, Arieli established that nanobubbles form on
flat hydrophobic surface of silicon wafers from dissolved gas
(Arieli and Marmur, 2011) and that these nanobubbles expand
and detach to form free-floating bubbles after decompression
(Arieli and Marmur, 2013a;Papadopoulou et al., 2015). This
establishes a link between stationary nanobubbles on the blood
vessel wall and blood-borne bubbles which prepares the scenario
for decompression VGE.
The second step introduces cavitation in biological systems.
Hills studied various endothelial surfaces from sheep and
humans for their hydrophobicity, using a method based on
the angle of contact, and found distinct hydrophobic areas
(Hills, 1992). He concluded that the oligolamellar surfactant
lining and lamellar bodies were potentially important factors in
influencing bubble formation on vessel walls. Similarly, Arieli
showed that the production of bubbles after decompression of
ovine blood vessels is associated to active hydrophobic spots
(AHS) that stain for lipids (Arieli and Marmur, 2013b, 2014)
and confirmed that these AHS consist of deposit of hydrophobic
lipids similar to or even originating from lung surfactant
(Arieli, 2015).
Arieli was then able to visually observe the whole dynamics
of bubble growth, detachment and the rate of bubble production.
He derived a mathematical equation for conditional detachment
which he based on buoyancy, and therefore, on reaching a critical
bubble volume (Papadopoulou et al., 2015;Arieli and Marmur,
2017). He concluded that decompression bubbles in divers can
develop only from pre-existing gas micronuclei (Arieli and
Marmur, 2017), and that these could be nanobubbles appearing
on active hydrophobic spots (AHS) as found on the endoluminal
surface of blood vessels.
Studies on diver pre-conditioning have confirmed that stable
stationary bubbles are most probably already present in the
diver before the dive. This pre-existing bubble population can
be affected by vibrations (Germonpre et al., 2009), exercise
(Dujic et al., 2004;Castagna et al., 2011), sauna (Blatteau et al.,
2008), and oxygen breathing (Castagna et al., 2009) before
the dive. This population can also be modified by drugs that
change endothelial function (Wisloff et al., 2004). All these pre-
conditioning protocols reduce bubble formation and/or growth
as demonstrated by reduced VGE levels measured after the dive.
These experiments raise two questions:
•How could a small gas phase exist and remain stable during
the ordinary life of a person before he becomes involved in
a dive?
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•How can factors such vibrations, exercise, heat, oxygen
breathing, and endothelial-modulating drugs interfere with
the bubbling process?
Recently, we showed (Balestra et al., 2016b;Germonpre and
Balestra, 2017) that pre-dive vibrations better protect the diver
than pre-dive oxygen breathing in terms of post-dive VGE count.
We also observed that preconditioning with oxygen breathing
before or during vibration is less efficient than vibration alone.
In this paper, we attempt to define a coherent system of
assumptions that can:
•Describe a stable gas phase compatible with the
properties of pre-existing bubbles involved in diver
preconditioning experiments,
•Explain the differences observed between various
pre-conditioning protocols.
For this purpose, we derive a simple mathematical model
for the stability of such gas phase that provides an equilibrium
equation based on local tissue metabolism. We then test
the resulting equation against our previously published data
(Balestra et al., 2016b) and the general literature to validate
its predictions.
METHODS
Our theoretical approach is based on two identified dimensions
of the problem, mechanical action related to vibrations, and
metabolism, which we suspected was physically acting behind
the scene through the “tissue inherent unsaturation” (Hills and
LeMessurier, 1969;Hills, 1970).
To fill the gap between ex-vivo experiments and actual
dives monitoring, we introduce metabolism as a parameter,
characterizing any living organism. We postulate that metabolism
can sustain a population of small gas pockets in the diver’s tissues
before he starts his dive. We give those gas pockets the name of
“Static Metabolic Bubbles” or SMB.
When considering these hypothetic SMB, the first problem
is the stability of such gas phases. In a stable situation, because
of surface tension, there must be a pressure difference between
the sum of the gas partial pressures in the gas phase and the
surrounding (ambient) pressure. The source for this pressure
difference must be identified and quantified because it bears
implications on the size of the gas phase and its possible evolution
during decompression.
The second problem is the shape of this gas phase and the
computation of its interfacial energy. Laplace’s law can only be
used in configurations, where explicit curvatures can be defined,
like for a sphere or a conical crevasse (Chappell and Payne, 2007),
a characteristic that cannot be assumed for these biological gas
pockets – of unknown shape. An alternative approach must be
defined to account for surface tension.
The Condition of Stability
We start with a stabilization condition for the initial metabolic
bubbles. Any gas phase in a tissue of a diver at the surface
should contain an inert gas (nitrogen), metabolic gases (oxygen,
CO2) and water vapor. The stability of this gas phase first
depends on the dynamics of gas exchanges through its surface.
Because the diffusivity of metabolic gases is high, the gas
exchanges are rapid (Van Liew, 1962) and we can reasonably
assume that the gases in the bubble are in equilibrium with
the adjacent medium. We define the adjacent medium as
the venous side of the tissue as all the studies that could
analyze gas concentrations in decompression bubbles have
measured values close to the venous ones (Ishiyama, 1983;
Foster et al., 1998).
The rationale for the stability equation is based on the gas
solubility in liquids described by Henry’s law. For a dissolved gas,
at equilibrium, at constant temperature:
Pi=kH
ici(1)
where Piis the gas pressure above the liquid, cithe gas
concentration in the liquid and kH
i, Henry’s constant for the gas
in the liquid at body temperature. By convention, the dissolved
gas tension inside the liquid is defined as kH
ici.
In the presence of a gas phase, Henry’s law is written for each
gas dissolved in a diver’s tissue, considered to be in equilibrium
with venous blood, that has diffused inside a local gas pocket. The
equation below, derived by Van Liew et al. (1993), relates the gas
phase pressures (Pb) to the tissue gas tensions:
Pb=Pv,O2+Pv,CO2+PH2O+Pv,N2
=kH
O2cO2+kH
CO2cCO2+PH2O+kH
N2cN2(2)
Note that because CO2also combines into HCO−
3to form
an acid-base buffer system that maintains the blood pH, the
CO2concentration in the above expression only refers to
dissolved molecules.
The Inherent Unsaturation of Tissues
The stability of a gas phase requires a pressure equilibrium. At
this point, we hypothesize that metabolism, a purely physiological
variable, could be linked to the physical world of bubbles by
introducing the oxygen window (OW) as defined by Behnke
(1967), also referred to as the “inherent unsaturation of
tissues” by Hills and LeMessurier (1969).
The OW is a concept based on the “behavior” of metabolic
gases. In a living tissue, the concentration of oxygen decreases and
the dissolved CO2concentration increases, due to metabolism.
In terms of dissolved gas concentrations, the process is balanced,
as there is nearly a 1 to 1 ratio between oxygen consumption
and CO2production (this is the Respiratory Quotient, varying
from 1 to 0.8 at rest, depending on individual factors such as age,
activity and nutrition). In terms of dissolved gas tensions, there
is a significant difference as Henry’s constant for CO2is 20 times
higher than the one for oxygen. The decrease in oxygen tension
is much more important than the increase in CO2tension. As a
result, the sum of the gas tensions on the venous side becomes
lower than on the arterial side.
This difference between the sum of the venous tissue gas
tensions and the ambient pressure is called the OW. It quantifies
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the capacity of the body to take in, transport and deliver oxygen
to the tissue for a given activity. Its computation involves:
•Central factors such as alveolar ventilation, respiratory
quotient, cardiac output, hemoglobin concentration, Hb-
O2affinity and perfusion rate.
•Peripheral factors such as tissue local blood flow,
capillary density, oxygen extraction, oxygen diffusion
and tissue metabolism.
The OW is theoretically defined by the activity of the
mitochondria. Because pressures of metabolic gases are difficult
to measure at this level, the OW is more conveniently defined
across the arterial and venous sides of the tissue, for which
concentrations of metabolic gases are well documented. In this
work, we define the OW as the pressure difference between the
ambient pressure and the tissue venous gas phase pressure as in
the above-mentioned Van Liew publication:
OW =Patm −Pb=Patm −Pv,O2+Pv,CO2+PH2O+Pv,N2
(3)
The gas phase described in Eq. 3 is not at pressure equilibrium
and must evolve toward a new state according to the second
principle of thermodynamics. The ambient pressure and partial
pressures of constituting gases being fixed, the only solution for
the system to cope with the OW is to create interfacial energy.
The Classic Thermodynamic Approach
to Bubble Stabilization
In Gibbs (free energy) thermodynamics, the modeling of
gas supersaturated liquids requires computing the interfacial
energy. Authors have proposed models, where bubbles are
stabilized by Laplace’s law, a skin of surfactant at the
liquid/gas interface (Yount, 1979b), a diffusion barrier (Yount,
1979a), tissue elasticity (Goldman, 2010), or combinations of
the aforementioned.
Using Laplace’s law to express the interfacial energy between
the liquid and the gas phase requires defining the curvature of the
interface. For the simple case of a spherical bubble equilibrated
with venous tensions it is classically expressed as:
Patm −Pv=2γ
r(4)
where γis the surface tension, r the bubble radius and Pvthe
bubble internal pressure.
For a spherical bubble attached to a flat substrate, where θ
is the contact angle and αthe base surface radius, it becomes
(Yount equation):
Patm −Pv=2γcos(θ)
α(5)
Explicit mathematical solutions have also been proposed for a gas
phase located in a conical crevasse (Harvey et al., 1944;Tikuisis,
1986;Chappell and Payne, 2006).
In theory, for more complex configurations, splitting the
interface into smaller elements of known curvatures should allow
applying the Laplace’s law by finite element calculations. In
practice, the difficulty is to define a geometry, especially for small
bubbles where the interfacial energy becomes pre-dominant.
Large discrepancies have been reported between the predicted
internal pressure of a nanobubble and the actual measurement
in physical systems (Ohgaki et al., 2010). The differences are
expected to be even worse in biological systems because of the
complexity and variability of living organisms. We therefore
looked for an alternative formulation of the interfacial energy,
avoiding any geometrical description.
The Non-extensive Thermodynamics
Approach to Bubble Stabilization
Non-extensive thermodynamics was developed to describe the
behavior of solid and liquid condensates at the nanoscale, without
having to refer to geometrical considerations. We chose the
concept because it replaces curvature by volume and greatly
simplifies our approach. It also applies without restrictions
to nanometric as well as micrometric systems. The difference
between the internal and external pressures of the above gas phase
can be written as (Turmine et al., 2004):
Patm −Pb=mτα 1
V1−m
b
(6)
where Vbis the volume of gas and αa coefficient related to the
system. The coefficient τis an intensive variable that characterizes
the interface similarly to the surface tension. It can be negative or
positive which means that the system can be stabilized by either
a negative or positive pressure difference, similarly to inward or
outward curvature in Laplace’s law. The coefficient m represents
the “thermodynamic dimension” of the system and is smaller
than one. It somehow describes the shape of the system. For
instance, setting τ=γand m= 2/3 allows turning the above
expression back to Laplace’s equation for a spherical bubble.
The Static Metabolic Bubbles Volume
Equation
We combine Eqs 3 and 6 to establish the condition of stability and
obtain an original equation linking the OW to the stabilization
energy of the SMB.
OW =mτα 1
V1−m
b
(7)
The above condition of stability demonstrates that:
•Metabolism can stabilize small gas pockets through the
tissue inherent unsaturation;
•Metabolism controls this initial gas pockets volume.
The only requirement is a site with favorable thermodynamic
conditions to generate a nanobubble that will evolve into a stable
SMB. This pre-existing SMB population in living organisms
becomes a direct consequence of metabolism:
•Metabolism provides the inherent tissue unsaturation
required to stabilize the SMB.
•Metabolism is a continuous process that can sustain this
SMB population over time.
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•Metabolism can regenerate the SMB if the conditions are
changed, provided the hydrophobic sites are persisting
(Wienke and O’leary, 2018).
Linking Metabolic Gas Pockets and
Vascular Gas Emboli
Once the diver enters a decompression state, the dynamic of gas
exchanges will feed the SMB by diffusion from the adjacent tissue
(Van Liew et al., 1993). The SMB will grow until it reaches a
critical volume for bubble detachment and generate blood-borne
bubbles. The level of VGE detected in the divers will therefore
depend on three parameters:
(1) The density of active sites.
(2) The initial SMB volume; this will define the time it takes for
an SMB to grow to its critical volume of detachment, and
thus determine the delay for the first bubbles to appear.
(3) The rate of ascent that will create the diffusion
gradients and define the rate at which SMB grow and
VGE are produced.
RESULTS
This paper consists in developing the consequences of a
mathematical hypothesis and does not bring any original
experimental results. It, however, refers to a long series
of experiments we conducted on divers pre-conditioning
(Germonpre et al., 2009;Balestra et al., 2016b;Germonpre
and Balestra, 2017) for which explanations will be presented
in the discussion.
Estimation of the Oxygen Window
We calculated the theoretical OW based on Egi’s model (Egi,
1994). At surface, the inherent unsaturation is estimated at
70 hPa. At depth, tissue oxygen depends on the diver’s inhaled
oxygen partial pressure. An increase of the pO2in the breathing
gas drastically influences the OW. This increase is linear until a
point where the amount of dissolved oxygen is such that the tissue
only consumes the dissolved oxygen and the hemoglobin remains
maximally saturated. In this model, this point is achieved at
around 2,200 hPa of pO2,which corresponds to a diver breathing
pure oxygen at a depth of 12 m. Beyond this point – which
exceeds operational diving limits – the OW levels out at around
2,200–2,300 hPa (see Figure 1).
Estimation of the Static Metabolic
Bubbles Volume
Following the determination of the OW, Eq. 7 theoretically
permits calculating the gas phase volume. However, the
coefficients used in the formula cannot be defined numerically
because of the lack of experimental data. To obtain an estimation,
we adapted Eq. 7 to spherical bubbles by combining Eqs 4 and 6
to obtain:
OW =2γ
r(8)
This way, using a surface tension of 0.050 N.m−1(Van Liew
and Raychaudhuri, 1997) and two extreme values of the OW for
diver breathing air at surface and a diver breathing pure oxygen
at 12 m, we calculated a bubble radius ranging from 0.45 to
14 µm (Table 1).
The bubbles radii obtained are too large to be physiologically
relevant. For a diver at surface, the bubble radius would
correspond to 4 times the radius of a red blood cell and
would not fit into a small blood capillary without seriously
impairing the blood flow. This simply demonstrates that
SMB are most probably not spherical and fully justifies our
choice of Non-extensive thermodynamics based on volume
rather than on radius.
DISCUSSION
Limits to the Model: Sites for Static
Metabolic Bubbles
Equation 7 is a static equation that does not carry any information
on the initial growth of the SMB. It simply defines their stability
once they have formed and reached a given size. It ignores the
nucleation process and growth.
Equation 7 also does not bring any indication on the
location nor the geometry of the sites (crevices, flat surfaces,
and hydrophobic spots). It does not exclude any possibility
either. It remains compatible with gas bubbles attached
to hydrophobic surfaces on the vessel endothelium as
described by Arieli.
With regard to the availability of these sites, we identify three
parameters to characterize a given diver at surface, prior to a dive:
(1) The SMB population depends on the number of available
sites for nucleation. For consistency with Arieli’s work, we
FIGURE 1 | Oxygen window computed according to Egi’s model.
TABLE 1 | Estimated radius of spherical SMB for two diver situations.
OW Spherical SMB radius
Diver at surface breathing air 70 hPa 14 µm
Diver at 12 m breathing pure oxygen 2200 hPa 0.45 µm
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considered hydrophobic sites located on the blood vessel
endothelium. Therefore, for a given diver, we define a first
parameter corresponding to the site density, that is the
number of sites available per unit of tissue volume. This
site density is a long-term characteristic that may evolve
with age, as does metabolism (Cialoni et al., 2017).
(2) Because all the available sites may not be populated at all
times, we further define the AHS, corresponding to sites
actually occupied by a SMB. The effective AHS density
depends on the recent history and condition of the diver,
such as pre-conditioning interventions, or several dives
with sufficient surface interval.
(3) The diver is finally characterized by the volume of his SMB
population. According to Eq. 7, this volume depends on
the tissue metabolism. It also depends on the inspired pO2
which much influences the magnitude of the OW.
For what concerns decompression, our understanding is that
SMB could be present in any place that fulfils two conditions: a
favorable physical site and enough tissue super saturation. Arieli
observed in his first experiments that bubbles could generate
from a silicon wafer, a purely physical support (Arieli and
Marmur, 2011), but this required a high gas gradient created by
decompression. In his following ex-vivo experiments, the tissues
had no metabolism and the bubble formation remained purely
physical even if they involved real tissues as a support. In divers,
our mathematical derivation of the SMB stability considers the
venous side of a tissue. However, it is admitted that SMB could
form as well in the lymphatic vessels (Hugon et al., 2009;Balestra,
2014b) or the distal arterial tree (Arieli and Marmur, 2017).
Limit to the Model: Size of the Static
Metabolic Bubbles
The problem of identifying the gas micronuclei traditionally
associated to decompression bubbles has recently been reviewed
by Doolette (2019). He stressed the contradiction between the
nanobubbles described in the physical chemistry literature and
the physiological conditions of decompression, in particular,
the extreme internal pressure calculated by Laplace’s law for a
small spherical bubble. If the existence of SMB still remains
hypothetical, their description avoids at least two pitfalls. First,
they have no defined shape, just a volume, and therefore escape
Laplace’s law (applicable only to a spherical bubble). Their
interfacial energy can be much lower, as one could imagine
when figuring for instance a tubular bubble. Secondly, their size
is larger. These gas pockets are expected to have evolved to
an intermediate volume set between the nanobubbles initially
cavitating at the AHS and the critical volume bubbles that detach
from these AHS to become VGE.
At surface, we could consider that various tissues in the diver’s
body will have different metabolic rates. Therefore, prior to the
dive, it would be reasonable to expect a distribution of initial SMB
volumes rather than a single definite OW and volume of SMB.
The formulation in Eq. 7 is therefore, a simplification.
During descent, the SMB volume will be reduced according to
Boyle’s law. However, our assumptions do not allow us to decide
whether there exists a crushing pressure for the collapse of the
SMB as postulated by Yount (1979b).
Limits to the Model: The OW Formulation
We have used Egi’s model of OW, where the role of CO2
is minimized. This is based on the fact that there is no
“CO2window” because CO2dissolves into HCO3, a weak
acid responsible for buffering the blood. The venous pCO2is
considered constant. On this basis, when the diver performs
exercise, he increases his tissue metabolism and oxygen
consumption, but the mathematical description shows that the
OW remains almost unaffected because of the large availability
of oxygen in the arterial side. With such a model, the influence
of exercise on the tissue OW is small (a few hPa) at surface and is
negligible in diving conditions up to 2000 hPa of inspired oxygen.
Other definitions of the OW exist depending on the
assumptions considered. For instance, Kot et al. (2015)
defined the OW using tissue metabolic gases values. This
provided a higher estimate of the OW that they called the
extended oxygen window.
Van Liew developed an improved OW model by taking into
account CO2variations with exercise (Van Liew et al., 1993)
and the influence of CO2on the oxygen dissociation curve.
An increase of the Pv,CO2 in Eq. 3 decreases the tissue OW.
Consequently, according to governing Eq. 7, it results in a larger
volume SMB. A high level of tissue CO2could be the explanation
to the findings of Wilbur et al. who detected, at surface, with a
dual frequency ultrasound, a signal consistent with microbubbles
after intense exercise on an ergonomic bicycle in a human
subject’s leg (Wilbur et al., 2010) without any decompression.
Another improvement on the OW calculation was proposed
by Walsh et al. who introduced the Michaelis Menten equation
to describe the kinetic of oxygen uptake (Walsh et al., 2017).
This relation allows computing a local non-linear oxygen
consumption and accounts for the fact that different tissues may
have different metabolism and therefore different OW’s. It could
be the way to a more realistic computation of the OW based on a
Gaussian distribution of tissue and individual metabolisms.
Decompression: Relation Between
Metabolic Gas Pocket and Vascular Gas
Emboli Detection
We refer to the scenario proposed by Arieli and Marmur (2017),
where the SMB are activated by decompression and grow until
they release as a VGE in the blood stream, after the bubble has
reached a critical volume of detachment. If buoyancy is the drive,
it means that this critical volume of detachment is independent
of the physical shape of the site and is a constant for every diver.
This scenario depends on the dynamic of gas exchanges
because the surrounding tissue feeds the SMB, causing growth
until it reaches its critical volume. After the first bubble has
detached, the site will continue producing bubbles as long
as gases will diffuse into it. This suggests that larger initial
SMB detach more easily than smaller ones because they can
reach this critical volume more rapidly (for the same local gas
gradient). Therefore, the initial SMB volume is the first parameter
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Imbert et al. Static Metabolic Bubbles in Divers
controlling VGE once the diver is involved in decompression.
This volume in turn depends on the tissue OW according to Eq. 7,
which then refers to the diver’s metabolism. The interdependence
between number of active spots and initial SMB volume could
be the reason for the variability in VGE production observed
between divers (Balestra, 2014a;Germonpre and Balestra, 2017;
Papadopoulou et al., 2018).
Variation of Metabolism: Influence of Age
and Fitness on Vascular Gas Emboli
Detection
Metabolism is known to decrease with age. According to Eq. 7, a
decreased metabolism, associated to a reduced OW, should yield
larger volume initial SMB. This could explain the higher levels of
VGE detected in older divers (Carturan et al., 1999;Cialoni et al.,
2017). Metabolism therefore introduces age as a first individual
characteristic for a diver involved in a decompression.
Metabolism is known to be linearly related to cardiac
frequency in rest (Kang et al., 2017). Also, the all-encompassing
law of Kleiber has shown a linear relationship between the log
of metabolism and the body mass (Kleiber, 1947). These factors
suggest that fitness increases the OW (Painter, 2005). According
to Eq. 7, an increased metabolism, associated to a higher OW,
yield smaller volume SMB. A smaller gas phase takes a longer
time to detach and produce fewer circulating bubbles during
the decompression time. This would explain the lower levels
of VGE observed in fit divers. Metabolism therefore introduces
fitness as a second individual characteristic for a diver involved
in a decompression.
The action of age and fitness are opposed and independent but
can combine in each diver to produce variability. On one hand,
an old and sedentary diver should have larger volume of initial
SMB than a young and fit diver and produce more VGE. On the
other hand, an old but fit diver could produce less VGE than a
younger but sedentary diver.
In a recent large-scale database analysis, DAN Europe (Cialoni
et al., 2017) concluded that only two factors, increased age
and BMI, could be related to increased bubble formation. They
also noted that neither height or weight separately had any
relation to the bubbles. It is tempting to associate BMI to fitness
for this divers’ populations because it would then provide the
confirmation that because age and fitness act on the metabolism,
they in turn acts on the OW and finally control the individual part
in the bubbling process.
Decreased Metabolism: Influence of
Bedrest on Vascular Gas Emboli
Detection
Confirmation of the above analysis is provided by a bedrest
experiment recently published by Gennser et al. (2018). Authors
used a 35 days’ bedrest conditioning to simulate microgravity and
then ran several air dives to simulate extra vehicular activity. The
dives were performed with divers still in bedrest conditions and
were controlled by bubble Doppler monitoring. They concluded
that 5 weeks of bedrest significantly increased bubble grades
after decompression.
The analysis of this experiment using our model is coherent
with the reported results:
•Bedrest conditions are associated to minimal activity and
therefore to a minimal metabolism. The consequence is that
the initial SMB volume in the divers prior to the dive was
maximal according to Eq. 7.
•Then, the lack of exercise reduces vibrations and it is likely
that most of the available AHS were populated by SMB.
•After a bedrest, the divers started the dive with a high
density of SMB with a maximal volume that favored higher
grades of detected VGE.
Vibrations Preconditioning: Influence on
Vascular Gas Emboli Detection
Preconditioning with vibrations produces a local energy release.
The energy transferred will move the system to another
equilibrium state. In this new state, changes in the internal
pressure of the gas phase will modify its volume by either
compression or temperature change and/or loss of gasses by
diffusion. This will challenge its stability and the SMB may
reach the critical volume and detach from its support. The main
role of vibrations seems to reduce the number of AHS. The
consequence of vibrations alone will be less VGE measured after
decompression. However, vibrations do not affect the metabolism
and therefore do not change the SMB volume according to Eq. 7.
Divers preconditioning experiments have shown that pre-
dive vibrations reduce the number of VGE after decompression
(Balestra et al., 2016b). Figure 2 shows VGE counts from this last
paper, expressed in number of bubbles detected per heartbeat, at
rest and after a leg flexion, for the control dives and the dives with
pre-conditioning with vibrations and oxygen.
The protocol of VGE detections, with either Doppler or
echocardiography, includes first a measurement at rest and then
a measurement after a squat or leg flexions. The flexion generally
triggers a rush of circulating bubble provoked by the muscular
contractions. Referring to our model, it suggests that this flexion
causes SMB to be dislodged from their sites before reaching the
critical volume of detachment.
Data in Figure 2 shows that there is no significant
difference between rest and flexion after vibration and
oxygen preconditioning. For the vibration preconditioning,
the explanation could be that SMB have already been
dislodged before the dive, so the muscle contraction applies
to a smaller number of SMB and produces less VGE
(Germonpre and Balestra, 2017).
Data in Figure 2 may allow quantifying this protective effect
in term of VGE count reduction, and may make it possible to
define simple models and adjust coefficients by data fitting to
predict the site density and initial SMB volume of a given diver
or group of divers.
Exercise Pre-conditioning: Influence on
Vascular Gas Emboli Detection
Pre-conditioning with exercise is complex because exercise
combines several effects. It increases metabolism and shear stress
along the endothelium. It also produces a series of metabolic
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FIGURE 2 | Maximal bubble counts before and after leg flexion using
transthoracic echocardiography in 6 healthy divers known as consistent
bubblers after a 33 m/20 min dive. The bubble maximal number is measured
at 30 and 60 min post-dive. Both rest and post-flexion measurements are
significantly lower with vibration pre-conditioning than with oxygen
pre-breathing. Rest and post-flexion bubble counts are not significantly
different in oxygen pre-breathing dives and in vibration pre-conditioning dives
(Wicoxon matched-pairs signed rank test) redrawn from Balestra et al.
(2016b).
changes: vasodilatation, heat production, PCO2increase and
dehydration. Finally, it causes mechanical vibrations.
This principle of vibrations pre-conditioning from the above
paragraph can be extended to exercise pre-conditioning if the
metabolic response is ignored. The dose of vibrations obviously
varies with the type of activity and this suggests that different
exercises may have different efficiencies. For instance, running
or mini-trampoline should be more efficient than swimming or
cycling. Moreover, considering that the metabolism regenerates
the SMB progressively, the frequency of the sport activity
becomes important. In fact, the selection of the sport and the
frequency of its practice define something we like to call an
“healthy life style” (Thompson and Batterham, 2013), which has
been suggested to be of importance to reduce diving DCS risk
(Carturan et al., 1999, 2002).
Oxygen Breathing Pre-conditioning:
Influence on Vascular Gas Emboli
Detection
Divers pre-conditioning experiments have shown that
pre-dive oxygen breathing reduces the number of VGE
after decompression.
Pre-dive oxygen breathing first involves de-nitrogenation and
could protect the diver by reducing his tissue inert gas load
before the dive. This protection is relative as it only concerns
790 hPa of surface PN2compared to a bottom PN2that could
be five times larger.
According to our model, pre-dive oxygen breathing drastically
increases the OW and reduces the SMB volume. Smaller volume
SMB will take a longer time to grow and reach the critical
volume for detachment and so will result in less VGE (Figure 2).
This was confirmed by Van Liew who published that pre-dive
oxygen breathing protects rats from decompression bubbles (Van
Liew, 1998). However, pre-dive oxygen breathing is not expected
to act on the density of SMB sites as vibrations would do
(Blatteau et al., 2012).
Combined Vibrations and Oxygen
Breathing Pre-conditioning: Influence on
Vascular Gas Emboli Detection
The results (Balestra et al., 2016b;Germonpre and Balestra,
2017) of the combination of vibrations and oxygen breathing
in our pre-conditioning experiment showed that in term of
post-dive VGE:
•Vibrations better protect the diver than pre-dive
oxygen breathing.
•Combination of oxygen breathing before vibration is less
efficient than vibrations alone.
Based on our model, these results can be explained by the
following contribution of factors:
•On the one hand, vibrations reduce the initial population
of SMB but do not change their size. Vibration is efficient in
reducing the number of VGE detected after decompression.
•On the other hand, oxygen breathing increases the OW
and according to Eq. 7, reduces the SMB volume. Smaller
SMB will take a longer time to reach the critical detachment
volume and will detach less easily. Pre-dive oxygen
breathing is efficient in reducing the number of VGE
detected after decompression.
•When combining the two above factors, if oxygen breathing
comes first, the SMB will become smaller and more difficult
to detach. The consequence will be that the same squeezing
action (legs flexion) will detach only the biggest SMB after
oxygen breathing than just alone keeping a higher number
of VGE. The overall benefit will be less (Figure 2).
Our model suggests that oxygen breathing and vibrations can
counteract their effects in this sequence. Alternatively, it proposes
that the best pre-conditioning sequence would be to first expose
the diver to vibrations to reduce the SMB density and then reduce
the volume of the remaining SMB by oxygen breathing. However,
this remains to be experimentally tested.
Exercise or Stress During
Decompression: Influence on Vascular
Gas Emboli Detection
The situation is different for the previous discussion because
change in the SMB population will occur during the dive.
In addition, several factors will overlap: metabolism, cardiac
function, heat/cold adaptation and exercise. The analysis
therefore proceeds with simplification by separating the issues.
With regards to activity during or after the dive, it is
understood that light exercise with little metabolic change but
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Imbert et al. Static Metabolic Bubbles in Divers
significant vibrations will release more circulating VGE according
to our model predictions. However, two situations may occur.
In a first situation, if the ascent is badly controlled during
decompression, or if the decompression table is inadequate, the
excess of bubbles dumped into the venous bed might overload
the lung and result in arterial bubbles and a higher risk of DCS
(Madden and Laden, 2009).
On the other situation, provided the excess bubbles are filtered
by the lung, exercise permits evacuating inert gas at a higher rate.
Since there is more gas inside a bubble than dissolved in the same
volume of blood, this results in a more efficient decompression.
Dujic et al. reported that during SCUBA diving, light exercise at
the 3 meters stop reduces post-dive VGE (Dujic et al., 2005) and
that post-dive exercise induces a more rapid VGE decline (Dujic
et al., 2006), indicating a faster decrease of tissue inert gas. Light
exercise is therefore beneficial for a decompressing diver. For the
same reason, commercial divers in saturation are encouraged to
perform a daily session of light exercise during decompression.
With regards to stressful situations during the dive, such as
cold or low visibility, they have shown to be statistically related
to higher risk of DCS (Cialoni et al., 2017), even if depth
and time of the dive were lesser. Stress by itself will trigger a
series of physiological reactions such as cardiac frequency and
ventilatory rate increase. It will also change the cellular oxygen
consumption and metabolic rate as a response to stress and
subsequent neuroendocrine reactions. The combined influence
of these factors may be as yet not precisely calculable, but will
(see Eq. 7) undoubtedly change the population of SMB, their
localisation and behavior during decompression.
Metabolism and Diet: Influence on
Vascular Gas Emboli Detection
There is a renewed interest in nutrition in commercial diving
to improve divers’ performances and eventually reduce their
oxidative stress (Deb et al., 2016). It has been suggested that the
diver’s diet has also a measurable effect on the level of VGE or on
the vascular wall compliance which may also influence the SMB
elimination (Theunissen et al., 2013, 2015;Valadao et al., 2014;
Balestra et al., 2016a).
Metabolism is affected by nutrition. There is a possibility to
link nutrition and metabolism through Eq. 7 because Egi’s model
includes the respiratory quotient in the definition of the OW. This
respiratory quotient could be used to link the diver’s diet directly
to the VGE production.
Implication of Static Metabolic Bubbles
on Future Decompression Algorithms
The link between the presence of VGE and the risk of DCS is
not direct. Even though Doppler monitoring has been used as the
principal endpoint for the development and validation of most air
tables (Spencer, 1976) and mixed gas tables (Nishi, 1991), large
scale studies have demonstrated that:
•Vascular gas emboli may be present in any decompression
without provoking any symptoms of DCS (so-called
silent bubbles).
•There is a large variability among divers in term of VGE
production (Papadopoulou et al., 2018).
•It remains that the lower the bubble count (or grade)
the lesser the risk of DCS (Nashimoto and Gottoh, 1978;
Gardette, 1979;Eftedal et al., 2007).
Linking VGE and the risk of DCS requires establishing a
bubble scenario. In 1908, J. S. Haldane stated that “If small
bubbles are carried through the lung capillaries and pass, for
instance, to a slowly desaturating part of the spinal cord, they
will there increase in size and may produce serious blockage
of the circulation or direct mechanical damage” (Boycott et al.,
1908). This scenario considers intravascular bubbles collected by
the venous system and eliminated at the lung level in normal
dive conditions. If a bubble passes into the arterial side, it may
reach a tissue and causes local ischemia, mechanical damages
and inflammation. The filtering capacity of the lung was first
studied by Hills (Butler and Hills, 1979). Failure of the lung
filter was proposed by James for the onset of CNS and spinal
symptoms (James, 1982;James, 1991). Shunting of the lung filter
explained the role of a patent foramen ovale (PFO) in the diver’s
susceptibility to Type II DCS (Moon et al., 1989;Wilmshurst
et al., 1989;Balestra and Germonpre, 2016;Lafere et al., 2017).
Finally, Hennessy published in 1989 all the physical aspects of the
arterial bubbles scenario in a paper that became the foundation
of the arterial bubble assumption (Hennessy, 1989).
We have adopted this scenario to link VGE and the
risk of DCS:
•The dose of incoming VGE and the lung filtration capacity
determine the possibility of arterial bubble occurrence
(Butler and Hills, 1979;Ljubkovic et al., 2012).
•The bubbles in the venous system trigger biological
reactions with the vascular endothelium that create
microparticles. These microparticles can pass in the arterial
system and provoke a tissue inflammation similar to
the one caused by bubbles (Thom et al., 2013, 2015;
Yang et al., 2015).
We therefore consider that arterial bubbles and microparticles
combine in the onset of DCS (Arieli and Marmur, 2017). The
dose of incoming VGE produced by decompression remains the
critical input to the lung filter.
The SMB assumption adds a step in the chain of events
triggered by decompression. This intermediate step corresponds
to a gas phase, located in the middle of scale, between
nanobubbles nucleating at the AHS and micrometric or
millimetric VGE dumped into the venous circulation.
Setting an acceptable level of decompression stress in a future
algorithm will require defining four additional parameters. The
first one will be estimate of the number and size of SMB, based on
the diver’ individual characteristics. The second parameter will be
the critical volume for bubble detachment that will control VGE
production. The third will be the lung bubble filtration function
that will determine the risk of passing arterial bubbles from the
input dose of VGE (volume and number). The fourth one will be
a risk function associating the number of arterial bubbles to the
risk of DCS symptoms. Further improvements could consider the
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Imbert et al. Static Metabolic Bubbles in Divers
evolution of the number of sites and SMB volumes with repetitive
diving and multi-days diving.
It makes it possible to supplement M-Values and gradient
factors to decompression algorithms based on an initial SMB
population adapted to the diver’s individual parameters.
The new algorithms will not necessarily produce much
different decompression profiles. The current profiles were
developed empirically but already provided an acceptable level
of risk. Most instances of DCS, however, occur within the limits
of these decompression profiles, for reasons as yet unaccounted
for. This model could provide a better control of conservatism
and offer the possibility to a given diver to select the level of
decompression stress he is ready to accept for a given dive.
The pre-existing gas pocket population (SMB) therefore,
becomes the diver’s main individual characteristic defining the
VGE level measured during or after a decompression. It may also
contribute to the other dimension of DCS, that is inflammation.
Bubbles that detach from their support can strip apart the AHS
as observed by Arieli (2017). The AHS may then reduce in size
or even disappear after a series of bubbles detachments. Arieli
used this possibility to explain divers’ acclimatization to intensive
and repetitive decompressions. We consider that when VGEs are
present, they could generate an inflammatory response because
the endothelium would be physically altered by the “rubbing”
effect of the VGEs. Causing some damage and retraction of
endothelial cells, exposing the endothelial basement membrane
to the blood and elicit interaction with inflammatory proteins
(Blatteau et al., 2018).
CONCLUSION
We postulated a pre-existing population of small static
bubbles in divers, located preferentially on hydrophobic
sites on the endothelial surface, populated and stabilized by
tissue metabolism.
These gas pockets are expected to have an intermediate
volume set between the nanobubbles initially cavitating at the
AHS and the critical volume bubbles that detach from these
AHS to become VGE.
We derived a stability equation linking the OW to the
metabolic gas pocket volume without having to define any
geometrical configuration.
We tested the assumption against our published experimental
data and other relevant papers and found that pre-existing SMB:
•Are consistent with the observations on ex-vivo tissue
bubble production by Arieli. This suggests that the level of
circulating VGE depends on two parameters: the number of
hydrophobic sites and the volume of the metabolic bubbles
populating these sites.
•Can explain the results of diver pre-conditioning
experiments using exercise, vibrations, oxygen breathing
and combined vibration and oxygen breathing.
•Could explain why the individual variations of detected
VGE in divers after decompression depend on the density
of AHS and therefore seem to be linked to age and fitness.
•Suggest that physical activity type and frequency control
this initial metabolic bubble population and therefore the
level of VGE produced during a given decompression.
In addition to specific individual factors, the diver’s “life
style” could influence the observed variations in post-
decompression VGE.
Our model links these small metabolic gas pockets to VGE
measurements and the potential risk of DCS. This model offers
two new possibilities for decompression algorithms (1) to adapt
decompression to the individual factors of a given diver and (2)
to select the level of acceptable decompression stress or DCS risk
for a given dive.
AUTHOR CONTRIBUTIONS
J-PI and SME developed the hypothesis. PG reviewed the medical
implications. CB developed the physiological part of the theory.
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Conflict of Interest Statement: J-PI was employed by company Divetech.
The remaining authors declare that the research was conducted in the absence of
any commercial or financial relationships that could be construed as a potential
conflict of interest.
The reviewer DC declared a shared affiliation, though no other collaboration, with
one of the authors SME to the handling Editor.
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