(Chest. 1999;116:488-503.)
© 1999
American College of Chest Physicians
Emerging Concepts in the Evaluation of Ventilatory Limitation During Exercise*
The Exercise Tidal Flow-Volume Loop
Bruce D. Johnson, PhD;
Idelle M. Weisman, MD, FCCP;
R. Jorge Zeballos, MD and
Ken C. Beck, PhD
*
From the Division of Cardiovascular Disease (Dr. Johnson), and the Division of Thoracic Disease (Dr. Beck), Department of Internal Medicine, Mayo Clinic and Foundation, Rochester, MN; Department of Clinical Investigation (Drs. Weisman and Zeballos), Human Performance Laboratory, William Beaumont Army Medical Center, El Paso, TX.
Correspondence to: Bruce D. Johnson, PhD, Division of Cardiovascular Diseases, Baldwin 2B, Mayo Clinic and Foundation, Rochester, MN 55905; e-mail: johnson.bruce{at}mayo.edu
 |
Abstract
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Traditionally, ventilatory limitation (constraint) during
exercise has been determined by measuring the ventilatory reserve or
how close the minute ventilation (
E) achieved during
exercise (ie, ventilatory demand) approaches the maximal
voluntary ventilation (MVV) or some estimate of the MVV
(ie, ventilatory capacity). More recently, it has become
clear that rarely is the MVV breathing pattern adopted during exercise
and that the E/MVV relationship tells little about
the specific reason(s) for ventilatory constraint. Although it is not a
new concept, by measuring the tidal exercise flow-volume (FV) loops
(extFVLs) obtained during exercise and plotting them according to a
measured end-expiratory lung volume (EELV) within the maximal FV
envelope (MFVL), more specific information is provided on the sources
(and degree) of ventilatory constraint. This includes the extent of
expiratory flow limitation, inspiratory flow reserve, alterations in
the regulation of EELV (dynamic hyperinflation), end-inspiratory lung
volume relative to total lung capacity (or tidal volume/inspiratory
capacity), and a proposed estimate of ventilatory capacity based on the
shape of the MFVL and the breathing pattern adopted during exercise. By
assessing these types of changes, the degree of ventilatory constraint
can be quantified and a more thorough interpretation of the
cardiopulmonary exercise response is possible. This review will focus
on the potential role of plotting the extFVL within the MFVL for
determination of ventilatory constraint during exercise in the clinical
setting. Important physiologic concepts, measurements, and limitations
obtained from this type of analysis will be defined and
discussed.
Key Words: dynamic hyperinflation • end-expiratory lung volume • exercise • flow limitation • ventilatory capacity • ventilatory limitation
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Introduction
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Cardiopulmonary
exercise testing (CPET) is increasingly being utilized in many clinical
settings for the diagnostic evaluation of dyspnea on exertion and
exercise intolerance.1
CPET provides an objective
assessment of functional impairment and is valuable in identifying
mechanisms of exercise limitation, typically of cardiac or pulmonary
origin.2
3
4
One challenging task in the interpretation of
CPET is the diagnosis of exercise limitation caused by ventilatory constraints. Assessing the degree of
ventilatory constraint (limitation) has traditionally been based on the
ventilatory reserve or on how close the peak minute ventilation
(E) achieved during exercise approaches the maximal
voluntary ventilation (MVV) or some estimate of the MVV (typically the
FEV1 multiplied by 35 or 40).
The ventilatory reserve is dependent on numerous factors, including the
following: (1) ventilatory demand, which is dependent on factors such
as metabolic demand, body weight, mode of testing, dead space
ventilation, as well as neuroregulatory and behavioral factors; vs (2)
maximal ventilatory capacity, which is affected by mechanical factors,
ventilatory muscle function, genetic endowment, aging, and
disease. Ventilatory capacity may also vary during exercise due
to bronchodilation or bronchoconstriction,5
and it is
dependent on the lung volume where tidal breathing occurs relative to
total lung capacity (TLC) and residual volume (RV; ie, the
regulation of end-inspiratory lung volume [EILV] and end-expiratory
lung volume [EELV]). In the latter case, breathing at a low lung
volume (near RV) limits the available ventilatory reserve due to the
shape of the expiratory flow-volume (FV) curve and the reduced maximal
available airflows, as well as a reduced chest wall compliance.
Conversely, breathing at high lung volumes (near TLC) increases the
inspiratory elastic load and therefore the work of breathing (WOB). The
breathing reserve using the MVV therefore only provides limited
information and does not provide insight on breathing strategy or the
degree of expiratory or inspiratory flow constraints. Understandably,
significant controversy thus surrounds the assessment of the
ventilatory reserve in part because of a lack of a definitive
measurement of ventilatory capacity.
More sophisticated techniques have thus been applied to assess the
degree of ventilatory constraint during exercise.5
6
7
8
9
10
11
These have included the following: increased dead space
loading12
; hypercapnic stimulation8
13
14
;
heliox administration15
16
17
; and negative pressure applied
at the mouth.10
However, these techniques also provide
little information on breathing strategy and, apart from the negative
pressure technique, tell little about the specific source of
ventilatory constraint.
Though not a new concept,18
19
20
plotting the tidal
exercise FV loops (extFVL) within the maximal FV envelope (MFVL) and
assessing the degree of expiratory flow limitation have been used by
several investigators to better assess and quantify the degree of
ventilatory constraint.5
6
7
8
9
12
14
21
22
23
This, of course,
is critically dependent on the placement of the extFVL within
the MFVL (to be discussed), but provides a unique visual index of
ventilatory demand vs ventilatory capacity. Although this technique is
gaining popularity as a means of assessing the degree of ventilatory
limitation, (and complementary to the traditional estimates of
breathing reserve) it remains technically more involved than
traditional estimates and indices of limitation based on the extFVL
need to be further defined, quantified, and assessed for utility in the
clinical setting.
The following review will focus on the potential role of plotting the
extFVL within the MFVL for determination of ventilatory constraint
during exercise in the clinical setting. Based on previous studies,
important physiologic concepts and measurements obtained from this type
of analysis will be reviewed and defined. Advantages and limitations of
the technique relative to traditional methods will be discussed, as
well as technical concerns when performing the measurements. Examples
of FV responses to exercise in health and disease will be examined, as
well as suggestions for further investigation.
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Information Gained From the extFVL/MFVL Analysis
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By aligning the extFVL within the MFVL, specific
information is provided on the following: (1) the degree of expiratory
flow limitation; (2) breathing strategy (ie, changes in
EELV); (3) elastic load, as represented by the EILV as a percent of TLC
(EILV/TLC) or the tidal volume (VT) relative to
inspiratory capacity (IC); (4) inspiratory flow reserve; and (5) a
theoretical estimate of the ventilatory capacity based on the EELV and
the maximal expiratory/inspiratory flows available over the range of
the tidal breath (ECAP).5
18
20
Definition of Expiratory Flow Limitation and EELV
The degree of expiratory flow limitation (or impending
flow limitation) during exercise has been previously expressed as the
percent of the VT (obtained from the extFVL) that meets or
exceeds the expiratory boundary of the MFVL5
7
8
(as shown
in Figure 1
). The degree of expiratory airflow limitation is therefore a balance
between ventilatory demand and ventilatory capacity combined with the
way subjects "choose" to regulate their EELV. The EELV differs from
the resting functional residual capacity (FRC) in that the FRC is the
lung volume achieved with a passive expiration and is thought to be an
equilibrium volume between the chest wall forces expanding the lungs
and the recoil forces of the lungs; the EELV, on the other hand, is
dynamically determined (dynamic FRC) based on expiratory and
inspiratory muscle recruitment and timing. A drop in EELV requires
expiratory muscle recruitment and has been proposed to optimize
inspiratory muscle length (for force development). In addition,
it helps keep the tidal FV loop on the linear portion of the
pressure-volume relationship of the lung and chest wall to reduce the
elastic load of breathing (keeps EILV at a lower percent of TLC),
provided that VT remains constant.7
24
25
In
addition, the energy stored (elastic and gravitational energy) in the
chest wall (rib cage, abdomen, and diaphragm) because of active
expiration may provide some passive recoil at the initiation of the
ensuing inspiration.24
25
26
On the other hand, a drop in
EELV that is too great will cause expiratory-flow limitation near EELV
due to the fall in maximal available air flow as lung volume decreases.
In most normal subjects (average fitness; < 35 years old; no
disease), EELV decreases with exercise, and expiratory airflow
limitation generally averages < 25% of the VT at peak
exercise workloads5
27
and generally occurs only over the
lower lung volumes, near EELV.
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Figure 1. Defining expiratory flow limitation. extFVLs are
aligned within the MEFL according to a measured EELV. The percent of
the tidal breath (VFL) that expiratory air flows meet or exceed
the MEFs are used as an estimate as to the degree of expiratory flow
limitation. ERV = expiratory reserve volume; IRV = inspiratory
reserve volume.
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Breathing Strategy (Regulation of EELV)
During exercise, in the absence of expiratory flow limitation,
EELV typically falls; however, when the degree of expiratory airflow
limitation becomes significant (> 40 to 50% of the tidal breath),
such as may occur with heavier exercise, EELV typically
increases,5
7
14
sometimes back to resting values or
higher (dynamic hyperinflation). This is not typically observed in
healthy individuals of average fitness and thus represents a change in
the normal breathing strategy during exercise. An acute increase in
EELV decreases inspiratory muscle length, increases the work and oxygen
cost of breathing, and decreases inspiratory muscle endurance
time.28
Thus the change in EELV (as noted above) likely is
another index of ventilatory constraint. This has generally been
expressed as a relative change from rest; however, it may be as
important to observe the change in EELV with increasing workloads,
because some subjects may demonstrate an initial decrease followed by a
substantial increase.7
Studies examining changes in EELV
with exercise have reported this as a change in EELV, IC, or
they have expressed the EELV or IC in relationship to fixed lung
volumes, such as the TLC or vital capacity (VC). The IC relative to VC
gives a good index of where subjects are breathing within their
operational limits.
Change in EILV
EILV is defined as the lung volume at the end of a tidal
inspiratory breath and is usually expressed as a percent of the TLC
(EILV/TLC). Studies that do not determine TLC express this as a percent
of full inflation volume VC, or may express VT relative to
IC. Previous studies have demonstrated that EILV reaches 75 to 90% of
TLC in heavy exercise in normal subjects.14
29
As EILV
approaches TLC, lung compliance begins to fall,29
and thus
the inspiratory elastic load increases. A high EILV (> 90%) relative
to TLC may also be a marker of ventilatory constraint and an index of
increased ventilatory muscle work.23
30
As ventilatory
demand increases and the subject increases EELV in order to avoid
expiratory flow limitation and to take advantage of the higher
available maximal expiratory airflows, EILV increases in order to
preserve the exercise VT. A failure to increase EILV
in the presence of significant expiratory flow limitation may represent
inspiratory muscle fatigue, inspiratory muscle weakness, or coexistent
elastic loading due to increased lung recoil or constraints imposed by
the chest wall. A breathing strategy where EILV does not increase with
increasing exercise intensity usually results in an increase in the
respiratory rate to augment ventilation. This strategy may initially
decrease the WOB, decrease intrathoracic pressure perturbations, and
alleviate unpleasant respiratory sensations associated with high lung
volumes. However, the increased breathing frequency causes
higher flow rates which, in turn, may further increase the degree of
expiratory flow limitation. This is an example where it is important to
examine multiple variables, including breathing frequency and degree of
dyspnea in order to accurately interpret the extFVL.
Inspiratory Flow Capacity
Few studies have investigated the degree to which inspiratory
flows approach inspiratory flow capacity during heavy
exercise.8
14
21
23
31
Because maximal inspiratory flows
are limited mainly by the ability of the inspiratory muscles to develop
pressure, it is likely that an index of exercise inspiratory flow
relative to maximal volitional inspiratory flows would provide an
assessment of inspiratory muscle constraint. The ability of the
inspiratory muscles to produce pressure (force) falls with higher lung
volumes (shorter muscle lengths) and higher flow rates (increased
velocity of muscle shortening).8
31
32
Previous
studies8
14
have suggested that the fall in the ability to
produce inspiratory pressure decreases from 0.65 to 0.97% for every
1% increase in lung volume above FRC, and decreases from 4 to 5% for
every 1 L/s increase in inspiratory flow rate above resting.
The lung volume where exercise inspiratory flow rates are closest to
maximal may not be where peak inspiratory flows are produced (typically
at mid to lower lung volumes), but may occur at the higher lung volumes
(70 to 85% of TLC) where demand for increased flow rates remains high
during exercise but where capacity is reduced due to shortened muscle
lengths.8
14
An example is shown in Figure 2
of the extFVL within the MFVL: the point where tidal inspiratory flows
come closest to capacity typically occur at the higher lung volumes
with heavy exercise (right, B), although at the lower
ventilatory demands (left, A), significant reserve is
observed throughout inspiration. A fall in maximal volitional
inspiratory flows (at a given lung volume) during or after
exercise would suggest inspiratory muscle fatigue, or less likely
a change in peripheral airway diameter33
or laryngeal
dysfunction (although patient effort may also contribute
significantly). Tidal inspiratory flows produced during exercise that
come close to or meet those obtained during maximal volitional effort
at rest would imply an inspiratory pressure demand near to
capacity.14
In normal subjects, flows during exercise
typically only reach 50 to 70% of the maximal volitional inspiratory
flows at the closest point during the inspiratory cycle (Fig 2
,
left, A).8
14
Expiratory flow limitation and a
rising EELV would clearly reduce the available inspiratory reserves if
VT remained unchanged (Fig 2
, right,
B).
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Figure 2. Inspiratory flow reserve. The capacity for
producing inspiratory flow declines at higher lung volumes (decreased
inspiratory muscle length). Tidal inspiratory flows thus (typically)
come closest to the maximal available flows at the higher lung
volumes. At the closest point along the inspiratory tidal loop,
flows usually only approach 50 to 70% of that which is available in
the average adult near peak exercise (left, A).
Expiratory flow limitation and a rising EELV (dynamic hyperinflation)
significantly reduces the inspiratory flow reserve (right,
B).
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Estimated ECAP
A number of techniques have been used to estimate a ventilatory
capacity.5
7
12
13
16
20
One technique
(ECAP) calculates a theoretical maximal exercise
ventilation based on the maximal available inspiratory and expiratory
airflows over the range of the tidal exercise breath placed at the
measured EELV.5
12
20
Such an estimate of
ECAP is not dependent on volitional effort to the
same extent as the MVV, and it takes into account the breathing pattern
and the dynamic changes in airway function (if MFVLs are obtained near
to the time the extFVLs are obtained). The methods used for the
determination of ECAP are shown in Figure 3
. Briefly, the extFVL is aligned within the MFVL according to the
measured EELV. The tidal breath is divided into equal volume segments
(
V; typically 50 segments). An estimated expiratory duration time
(TE) is determined by dividing each V by the average maximal
expiratory flow (MEF) within each volume segment and summing all such
times (
Te) over the expiratory phase of VT. Measured
inspiratory to total breathing cycle time is used to estimate
inspiratory time. The sum of minimal inspiratory time and TE gives a
minimal breathing cycle time and maximal breathing frequency. The
product of maximal breathing frequency and measured VT
equals ECAP. ECAP determined in
this manner has been shown to decrease with low level exercise in
normal subjects (secondary to a decrease in EELV) and to subsequently
increase significantly as VT increases through encroachment
on the inspiratory reserve volume.5
This technique
represents a true maximal ECAP for a given breathing
strategy. Typically, the ECAP will be related to the
degree of expiratory flow limitation; however, if no flow limitation
exists (ie, tidal expiratory flows do not meet or exceed the
maximal available flows at any point throughout expiration), this gives
an independent index of the available ventilation for a given breathing
pattern.
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The Traditional View of Ventilatory Limitation
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The traditional use of the MVV or some estimate of the MVV such as
the FEV1 multiplied by 35 or 40 relative to the
exercise ventilation as an assessment of breathing reserve has several
advantages. It provides a general (although variable) approximation of
ventilatory capacity, it is readily and widely applied, it is easily
understood, and it requires minimal analysis. However, the use
of the MVV to estimate the available ventilatory capacity during
exercise and to determine whether or not individuals have a mechanical
limitation to their ventilation has many shortcomings. For example,
Figure 4 illustrates the FV loops obtained while a subject performs the typical
12- to 15-s MVV maneuver vs the same subject exercising near maximum on
a stationary cycle ergometer. Significant differences exist in the
breathing patterns, highlighting the difference between a voluntary and
a reflex-mediated hyperpnea. Typically, the MVV is performed above the
resting FRC, EILV approaches TLC, and expiratory flows reach maximum
even at the highest lung volumes.34
Although not shown,
the expiratory pleural pressures needed to produce such high flows
early in expiration are excessive and over the mid to lower lung
volumes, often two to three times those necessary to produce maximal
flows. The high EILV/TLC greatly increases the elastic load to
breathing, and tidal inspiratory flows often equal those produced
during a maximal maneuver over a significant portion of the tidal
breath. Thus the MVV does not represent that pattern typically observed
or even available to the typical patient during
exercise.34
A previous study by Klas and
Dempsey34
in 1989 demonstrated that the WOB associated
with the MVV maneuver greatly exceeded that achieved when the hyperpnea
was reflexly driven as occurs during exercise. Other studies have shown
that the MVV cannot be carried out for > 15 to 30 s, confirming
the excessive work and cost associated with the
maneuver.28
32
34
Use of the exercise
E relative to the MVV also does not tell specific
information about the source or type of ventilatory constraint
(eg, expiratory flow limitation, inspiratory flow
limitation, or high inspiratory elastic load). The MVV also is
motivationally dependent, and it is unclear if a consistent
relationship exists between the exercise ventilation and the MVV that
represents enough ventilatory constraint to influence the
perception of dyspnea or exercise tolerance.
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Figure 4. MVV vs exercise hyperpnea. An example of the
difference in breathing pattern when the MVV maneuver is performed
(left) relative to the same subject near maximal
exercise (right) using a commercially available system
(Vmax; SensorMedics; Yorba Linda, CA). The MVV is performed at high
lung volumes (increased EELV) resulting in a high elastic load to
breathing and requires large expiratory pleural pressures to obtain the
high flows early in expiration (increasing the WOB). In contrast,
during exercise, EELV is reduced resulting in tidal breathing occurring
at a more optimal position of the pressure volume relationship of the
lung and chest wall with consequent less WOB (from R. Jorge Zeballos
and Idelle M. Weisman, William Beaumont Army Medical Center, El Paso,
TX).
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Plotting the extFVL within the boundaries imposed by the MFVL allows
specific assessment and quantification of the sources of mechanical
constraint, and it complements other measurements obtained during CPET
(eg, breathing frequency and VT). It
is not as motivationally dependent as the MVV maneuver, but it does add
a degree of complexity to the testing and analysis. The technique is
also highly dependent on accurate assessment of EELV, and although many
studies have reported reproducible measurements based on IC maneuvers
in various patient populations, its reproducibility in the typical
clinical setting remains to be determined. Improving technology has
minimized many of the difficulties in data collection; however,
precautions need to be taken to ensure the accurate placement of the
tidal loops, to correct for drift in flow signals, and to determine the
optimal maximal volitional FV envelope. These later issues remain
critical in the use of the extFVL to assess ventilatory constraint, and
they are reviewed in greater detail in the Appendix.
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Assessing Ventilatory Constraint Using the extFVL
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As the sophistication of conventional exercise systems improve, it
will become easier to measure and to assess the degree of flow
limitation as well as changes in EELV and EILV, with minimal changes in
the standard clinical exercise protocol. Conventional exercise
metabolic systems have evolved using the pneumotachograph, hot wire
anemometer, and turbine (bi-directional rotating vane) technology that
provide software to evaluate tidal breathing FV loops relative to a
MFVL. Although there are currently potential sources of error in these
systems and in this type of analysis, a careful systematic approach
will help eliminate many of these problems.
Baseline MFVL and EELV
The majority of studies using the extFVL to assess
E constraint have had subjects perform several
pre-exercise maximal expiratory and inspiratory maneuvers between TLC
and RV to define the reference MFVL. The largest MFVL is determined in
accordance with the American Thoracic Society standards (ie,
the MFVL with the largest combination of FEV1 and
FVC).35
In addition to performing these maximal maneuvers,
a series of four or five expiratory maneuvers performed between TLC and
RV at different efforts can be performed to help correct for possible
expiratory gas compression (see Appendix, "Defining the MFVL"
section). However, this adds an additional degree of complexity to the
testing and analysis, and its necessity in all patient populations is
undetermined.
To assess variations in EELV during exercise, several IC maneuvers are
also performed at rest until several reproducible measurements are
obtained. The initial instructions at rest are important for optimal
measurements of EELV during exercise. The resting FV loops are obtained
when the subject is relaxed and in a regular breathing pattern (several
tidal breaths are recorded prior to obtaining an IC maneuver),
typically with the subject in the standing or sitting position
(depending on the use of a treadmill or cycle ergometer).
Exercise Measurements
Most clinical exercise protocols consist of an incremental study
with stages of 1 to 3 min. Incremental changes in work intensity
require changes in breathing strategy as ventilatory demands increase
and constraints are approached. Plotting changes over the course of the
study will allow a detailed assessment of the breathing strategies
chosen. Constant work exercise studies are also becoming more frequent
in the clinical setting, as workloads may be sought that more closely
match the metabolic demands associated with tasks of daily living.
Unlike incremental exercise, the variations in ventilatory demand
during constant work exercise are limited unless the workload chosen is
of a sufficient intensity (nonsteady state).
Tidal exercise breaths can be obtained over the last portion
(eg, 30 s) of each exercise stage in the incremental
protocols (less frequent in fitter subjects or in stages < 2 min.).
Several tidal breaths are collected, followed by an IC maneuver to
determine any exercise induced change in EELV. To correct for possible
inequalities in inspiratory and expiratory volume due to drift, a
second IC maneuver is performed after 5 to 10 additional breaths (see
Appendix, "Measurement of the extFVL" section). MFVL maneuvers have
been used in conjunction with the IC maneuvers if there is concern over
the lability of airway tone (ie, bronchodilation or
bronchoconstriction during exercise). Performing the IC maneuvers or
even a single MFVL has minimal impact on measurements of oxygen
consumption (O2), carbon
dioxide production, and E if data are
obtained during exercise with averages 
30 s.7
8
14
Postexercise Measurements
We previously assessed MFVLs similar to baseline measurements
within the first 2 min after exercise to correct for a potential
bronchodilation that may have occurred during
exercise.8
14
Although significant changes were noted in
maximal expiratory airflow in older healthy adults (age, ~ 70 years
old), minimal changes were observed after exercise in healthy
younger subjects. A previous study by Warren et al36
in
1984 demonstrated that an exercise-induced bronchodilation persisted
for up to 4 min after exercise.
Plotting the Data
Reference MFVL: The best pre- and postexercise MFVLs
are plotted and set to TLC (or VC) to compare potential changes in
inspiratory and expiratory flow and volume. The MFVL with the largest
expiratory and inspiratory envelope is used for the reference loop. If
MFVLs were obtained during exercise, these can also be compared with
the pre- and postexercise MFVL to determine the largest reference loop,
or each extFVL can be referenced to the relevant MFVL produced during
exercise.5
Tidal Breaths: The tidal breaths prior to the IC or
MFVL maneuver obtained at rest or during each stage of exercise are
viewed (for outliers), computer averaged, and plotted within the
reference MFVL according to the measured IC.5
We have
previously performed the averaging of the tidal loops by dividing each
VT into 50 Vs and assigning a mean flow value.
The flow values are then averaged for each volume segment of each
VT and are plotted according to the mean VT and
measured EELV (TLC - IC).5
Previous studies have
averaged from 2 to > 20 tidal breaths for individual
subjects.5
8
14
This greatly reduces the breath-to-breath
variability and the potential for error.
Defining the Degree of Constraint
Ventilatory limitation has typically been viewed as an
"all-or-nothing" occurrence. However, past and present literature
suggests that the degree of ventilatory constraint incurred during
exercise is progressive.5
8
9
13
14
21
23
As the degree of
expiratory flow limitation increases, EELV typically rises (dynamic
hyperinflation) and the inspiratory elastic load increases. The degree
of constraint necessary to influence exercise performance or contribute
to the sensation of dyspnea is unclear.30
However, the
oxygen cost associated with breathing during exercise rises
dramatically as ventilatory constraints (eg, flow
limitation) are approached.9
Also, as ventilatory limits
are approached with exercise, the ventilatory response to increased
levels of inspired carbon dioxide or reduced levels of inspired oxygen
are reduced or absent.8
13
14
Thus, clearly the
constraints to flow and volume begin to contribute to limiting
ventilation and a rising cost of breathing prior to achieving a
ventilation that matches the MVV or which may result in a rise in
arterial carbon dioxide.
By defining and quantifying the suggested indexes of constraint, a more
precise assessment of the degree of mechanical limitation to breathing
can be applied. Using these indexes, the degree of constraint can be
defined as no or minimal constraint, mild, moderate, or severe rather
than the all-or-nothing assessment that is often associated with
the MVV (see Table 1
). Subsequent studies will be necessary to assess the validity of such
an assessment in various clinical populations. Use of hypercapnic
inspired air, dead space, and helium oxygen mixtures may help confirm
the validity of such an assessment to define the degree of constraint.
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Exercise Patterns in Health And Disease
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The following section will review the tidal FV responses to
exercise in various representative clinical examples contrasted with
responses observed in the healthy young and older adults. It should be
emphasized that the degree of ventilatory constraint is indeed a
balance between ventilatory demands and the available capacities. Thus,
even the healthy young adult may approach severe ventilatory
limitations, albeit at a metabolic and ventilatory demand that
far exceeds the patient populations.
Healthy Subjects
The ventilatory response to progressive exercise in the
typical, average, fit subject (age, 30 years; peak
VO2, 42 mL/kg/min; peak
E, 100 L/min) is shown in Figure 5
, left, A.5
14
Little change (from rest) was
noted in the expiratory boundary of the MFVL during or after exercise,
suggesting little change in airway caliber. Flow limitation was present
near peak exercise but over < 20% of the tidal breath and only near
EELV. EELV fell by approximately 0.7 L, and EILV increased to 80% of
the TLC. Exercise E expressed as a percent
of the MVV (estimated from FEV1 x 40) averaged
68% at peak exercise. By visual inspection, it can be seen that
substantial room exists to increase both flow and volume. Inspiratory
flow only approached 65% of the available inspiratory flow at the
closest point of the inspiratory phase. Thus, in young, healthy
subjects with average fitness, typically little ventilatory constraint
exists during exercise.
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Figure 5. Left, A: FV response to exercise in
the average fit healthy young adult during incremental exercise plotted
within the MFVL. In this population, EELV progressively decreases with
exercise, and expiratory flow limitation is only present near EELV over
a small portion of the VT. Considerable room exists to
increase ventilation even at peak exercise. Similar responses are also
shown for the fit aged adult (middle, B) and the young
endurance athlete (right, C). The older adult represents
a group of subjects with a mild decline in lung function but
maintenance of a high ventilatory demand. Flow limitation occurs at a
low work intensity and VE demand (40 L/min) and EILV at peak exercise
reaches a higher percent of TLC. This group has significant ventilatory
constraint at peak exercise. The fit young athlete (right,
C) represents a group of subjects with normal lung function but
excessive ventilatory demands. EELV initially decreases during exercise
like the average fit adult, but increases as significant expiratory
flow limitation occurs. By peak exercise in the majority of these
subjects, significant ventilatory constraint is observed similar to the
aged, fit adult.
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Healthy Aged
Aging causes mild to moderate declines in ventilatory capacity as
a result of decreased lung elastic recoil (the average
FEV1 of a 70-year-old person is 70% of that of
an average 25-year-old person). However, this is typically
balanced with a fall in demand (ie, decreased peak
O2 due to reasons
that are not fully appreciated (eg, decreased
maximal heart rate, muscle mass, etc).37
Figure 5
,
middle, B shows the mean tidal exercise FV responses in a
group of older subjects (age, 70 years old) with an exercise
capacity approximately twice age predicted (n = 29;
O2, 43 mL/kg/min;
E, 119 L/min) but similar metabolic and
ventilatory demands as the young average fit adult (shown in Figure 5
,
left, A) at peak exercise. Thus, this group of older
subjects represents a group with relatively high ventilatory demands
but with mildly reduced capacities. Flow limitation begins to occur at
a lower ventilation than noted in the younger subjects shown in Figure 5 , left, A (~40 L/min) and at peak exercise > 50% of
the tidal breath meets or exceeds the expiratory boundary of the MFVL.
EELV initially decreases but then begins to increase with these
moderate E demands. At peak exercise, EELV
is above the resting FRC, EILV reaches > 90% of TLC, and inspiratory
flows approach > 90% of the inspiratory flow capacity, indicating
little reserve available to increase E and
moderate to severe ventilatory constraint. In the more severely
constrained subjects, ventilation did not increase with increased
levels of inspired carbon dioxide during heavy
exercise.8
Endurance Athlete
To emphasize the fact that ventilatory constraint is not only
dependent on ventilatory capacities but also on ventilatory demand, the
average response to progressive exercise in group of endurance athletes
is shown in Figure 5
, right, C (n = 8, age, 25
years old; maximal O2, 74
mL/kg/min; peak E, 170
L/min).14
The young athlete represents a group with normal
pulmonary function (ie, lung volumes and flow rates) for
their age but with excessively high metabolic and thus ventilatory
demands. To date, there is little data to suggest that exercise
training increases maximal lung volumes or flow rates; however, the
ability to sustain a high E may be
increased.15
The responses are quite similar to the
average fit adult up to a ventilation of approximately 110 to 120 L/min
(ie, EELV falls; < 20% VT is
expiratory flow limited; tidal inspiratory flows < 65% of capacity;
and EILV < 80% TLC). However, with heavier exercise and the
increased ventilatory demands, expiratory flow limitation increases to
> 50% of the VT, EELV begins to increase
(approaching the resting FRC), and EILV approaches > 85% of the TLC.
Inspiratory flow rates with exercise are closest in proximity to the
maximal available inspiratory flow rates at 75% of TLC reaching 6.0
L/s and 95% of the available flow. In this particular group of
athletes, the addition of hypoxic and hypercapnic gases during maximal
exercise did not significantly increase E
further than that achieved breathing room air during maximal exercise,
implying a significant ventilatory load and moderate to severe
mechanical ventilatory constraint.
Moderate COPD
Patients with moderate airflow obstruction have a reduced
ventilatory capacity, and at rest, they may be hyperinflated with some
gas tapping.6
23
Figure 6
is an example of the typical response observed in a subject with
moderate airflow obstruction.6
22
23
30
As shown, EELV may
increase even with light activity due to the early degree of expiratory
flow limitation. Due to the steepness of change in the available
expiratory airflows, small increases in EELV (dynamic hyperinflation)
will yield significant increases in the available ventilation
(ECAP). By peak exercise, flow limitation is present
over the entirety of expiration, and inspiratory flows are produced
that nearly overlap the maximal inspiratory flows achieved immediately
after exercise. In addition, EILV approaches > 95% of TLC. This
particular subject had a near normal exercise tolerance for age, but
because of the reduced ventilatory capacity, he clearly could not
increase E further
(E/ECAP > 95%). In
patients with more severe COPD and marked hyperinflation, an increase
in EELV may not occur due to the very high VT/IC ratios at
rest and during low levels of exercise. In these subjects, the finding
that the extFVL coincides with the entire MFVL boundary at low levels
of exercise is not uncommon.18
22
23
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Figure 6. Patient with history of moderate COPD (forced
expiratory flow at 50% of VC = 35% of predicted for age): EELV
increases from the onset of exercise and expiratory flow limitation is
present over > 80% of the VT by peak exercise.
Inspiratory flows approach those available over the higher lung
volumes. Little room exists to increase ventilation.
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Interstitial Lung Disease
Patients with interstitial lung disease (ILD) have a reduced
VC and EELV at rest.21
38
An example of patients with a
history of ILD is shown in Figure 7
. Many patients with ILD have little room for an exercise-induced
decline in EELV (due to a reduced expiratory reserve volume and little
room for a marked increase in VT). Thus, they are
more dependent on an increase in breathing frequency (and flow) to
increase ventilation. In seven patients tested using the extFVL
analysis (peak O2
averaged 1.36 L/min; 57% predicted), the majority of patients did not
change EELV during exercise.38
Furthermore, significant
expiratory flow limitation and a high EILV/TLC was present in those
patients stopping exercise due to dyspnea, whereas no flow limitation
was observed in patients stopping exercise due to a complaint of leg
fatigue.12
This implies that expiratory flow limitation in
some of the ILD patients contributes to the dyspnea of exercise,
although additional studies would be necessary to corroborate these
findings. Interestingly, despite room to decrease EELV in the patients
that did not complain of dyspnea, EELV did not fall. It has been
suggested38
that hypoxemia in this population may play a
role in altering the more typical regulation of EELV (ie,
decrease expiratory muscle activity resulting in a higher EELV).
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Figure 7. ILD: Maximal and extFVL in patients with ILD.
Left: patients who stopped secondary to dyspnea.
Right: patients who stopped due to leg fatigue. Minimal
change was observed in EELV in either group, with the group complaining
of dyspnea demonstrated significant expiratory flow limitation (from
Marciniuk et al38
in 1994).
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Congestive Heart Failure
Patients with congestive heart failure (CHF) often have
restrictive changes in pulmonary function. Breathing pattern is altered
secondary to ventricular dysfunction, increased left ventricular size,
muscle weakness, and chronic pulmonary congestion. Although CHF
represents a heterogeneous population, recent studies in our
laboratory39
have demonstrated that many of these patients
breathe at rest near RV and are expiratory flow limited with little or
minimal exercise. Figure 8
is an example of FV responses (rest through peak exercise) in a
representative subject with New York Heart Association class III CHF
(from a study on 11 patients; average peak
O2, 17 mL/kg/min; peak
E, 56 L/min; ejection fraction
< 24%).39
It is unclear why these patients breathe at
reduced lung volumes, but it may be secondary to increased respiratory
drive and activation of expiratory muscles, or due to inspiratory
muscle weakness. Thus, it is possible that the breathing at the lower
lung volumes leading to dynamic compression of airways may contribute
to the increased dyspnea associated with exercise; however, like the
ILD patients, further studies would be necessary to determine more
formally the significance of the expiratory flow limitation.
Interestingly, in this patient population, the E/MVV
relationship remains within the normal range, suggesting little
ventilatory constraint; however, by plotting the extFVL within the
MFVL, the expiratory flow constraint is evident.
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Figure 8. Example of a patient with a history of CHF (New
York Heart Association class III). EELV is reduced at rest and remains
near RV throughout exercise despite significant expiratory flow
limitation and apparent room to increase EELV to avoid the flow
limitation.
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Additional Applications of the extFVL
In patients with single lung transplantation, EELV increases with
the encroachment of expiratory flow limitation (observed in four of
seven patients), whereas in patients with double lung
transplantation, a more normal decrease in EELV is seen with expiratory
flow limitation observed in only one of the patients
tested.22
Recent application of the extFVL analysis to lung volume reduction
surgery has demonstrated that successful lung volume reduction improves
lung recoil and respiratory muscle function as a result of a reduction
in dynamic hyperinflation (ie, 
EELV and EILV relative
to TLC).40
Studies have also used the extFVL to evaluate ventilatory constraint in
obesity and asthma.5
41
Interestingly, in the small number
of studies performed to date, the data suggest that some obese subjects
breathe at extremely low lung volumes at rest and often during exercise
despite significant room in the inspiratory reserve volume and
substantial expiratory flow limitation. The expiratory flow limitation
may contribute to the dyspnea in these obese subjects. Interestingly,
this is a group of subjects (like some of the heart-failure
patients shown) where the E/MVV relationship
suggests significant reserve, when in fact little room exists to
increase expiratory flow. Asthmatic subjects, using the extFVL analysis
during exercise, experienced greater expiratory flow limitation than
age-matched control subjects, but they attempted to defend ventilatory
reserve by altering bronchomotor tone and increasing
EELV.5
The use of the extFVL has also been applied to study mechanisms of
exertional dyspnea. Several authors23
42
43
44
have
demonstrated that dynamic hyperinflation manifested by an increased
EELV and EILV relative to TLC and the resultant increased respiratory
muscle impedance are major factors responsible for breathlessness
during exercise in patients with COPD. In patients with acute
bronchoconstriction, the fall in IC (
EELV) during exercise showed
the strongest correlation with increases in dyspnea and perceived
inspiratory difficulty. Patients also complained mostly of inspiratory
rather than expiratory difficulty.44
The extFVL analysis is also being used in the evaluation of therapeutic
interventions. The acute administration of inhaled albuterol
significantly reduced breathlessness during exercise in patients with
COPD as a result of decreasing dynamic hyperinflation (EILV/TLC and
EELV/TLC).23
In addition, there may be a clinical
utility to using the change in operational lung volume to determine
bronchodilator responsiveness in situations where resting spirometric
values do not change appreciably after bronchodilator
treatment.
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Current and Future Aims
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Over the last 30 years, little progress has been made in the
typical clinical setting in trying to better define mechanisms of
exercise intolerance and dyspnea, particularly when associated with the
possibility of mechanical constraints imposed by the respiratory
system. The classic MVV, while easily applied, is variable and has
proved to be limited in its overall usefulness of advancing our
understanding of ventilatory limitation during exercise. As such,
investigational studies have attempted other techniques to better
assess and quantify the specific type of ventilatory constraint
incurred during exercise. Among these techniques, plotting the extFVL
within the MFVL, defining specific indexes of constraint based on the
relationship of the tidal loops with the constraints imposed by the
maximal volitional FV envelope, and attempting to quantify the degree
of constraint have the potential to provide unique insights into the
role of pulmonary mechanics in the exercise intolerance in various
populations.
The technique can be easily integrated into the current CPET with the
addition of pre/postmaximal FVC maneuvers as well as tidal FV breaths
and serial IC maneuvers collected throughout the study. Critical
shortcomings include the ability of subjects to perform adequate IC
maneuvers for placement of the extFVL within the MFVL, and defining the
optimal MFVL to account for bronchodilation, possible compression of
airways, and/or bronchoconstriction. The use of the extFVL in
conjunction with other techniques, such as a negative pressure applied
at the mouth during expiration, may help circumvent the later potential
drawback. In addition, although specific indexes of constraint were
suggested, the optimal indexes to be used in clinical populations need
further studies and discussion for their utility in the clinical
setting. In addition, quantification of the degree of constraint based
on the proposed indexes and their association with the degree of
ventilatory limitation and symptoms needs further validation. A schema
that provides a scaling of the degree of constraint based on the
suggested indexes (eg, no limitation, mild, moderate, and
severe) may provide more information than the current trend which tends
to look at ventilatory limitation as an all-or-nothing phenomena;
however, this also needs further investigation.
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Appendix: Methods and Technical Concerns Regarding the extFVL
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Measurement of the extFVL
Most clinical exercise testing laboratories today employ automated
systems for measurement of gas exchange during exercise (eg,
E,
O2, and carbon dioxide
production). The majority of these systems use a device for measuring
flow (eg, pneumotachograph, mass-flow anemometer, turbine)
and integrate a flow signal to obtain volume. Few of these automated
systems, until recently, have offered continuous output of flow and
volume in order to obtain the tidal FV data necessary for plotting the
tidal exercise loops; and few, to date, have attempted to identify
sources of constraint or to quantify the degree of ventilatory
constraint when plotting the extFVL within the MFVL. Thus, the majority
of studies examining FV data have been investigationally
oriented.5
6
45
In these research studies, typically two
techniques have been used to measure the exercise FV loop: the wedge
spirometer (volume-displacement) or the flow-sensing
pneumotachograph.6
7
12
21
23
38
The spirometer and the
pneumotachograph as well as the other flow sensing devices each have
potential advantages and disadvantages for assessing flow and volume
during exercise; however, the majority can be used successfully if
appropriately calibrated and utilized.46–49
"Drift" is a problem with all flow/volume sensing devices. Drift
can occur in the signal due to electrical changes over time;
nonlinearities in the pneumo-tachograph, anemometer, or turbine
sensor; as well as physiologic changes (eg, temperature, gas
density, viscosity, and humidity).50
Thus, within a
breath, there may be significant variability in either inspiratory or
expiratory flow and volume. Slight differences in calibration between
the inspiratory and expiratory flow signal, acute changes in breathing
pattern, and/or a small drift in either or both phases of the
respiratory cycle will cause an unequal inspiratory to expiratory (or
vice versa) volume and a tidal FV loop that does not fully close or
meet (Fig 9
). Thus, developing appropriate corrections to account for
nonlinearities and accurate calibration as well as eliminating
physiologic changes (correcting for temperature and humidity changes)
will help eliminate drift.8
50
During exercise, small
amounts of drift (< 50 mL/min) can be corrected by performing
paired-IC maneuvers at the beginning and end of a recording
period.8
14
27
Assuming maximal inhalation volume is equal
(TLC) during both maneuvers, the peaks can be aligned by performing an
interpolated volume correction between the two points. An example of
drift correction by aligning two IC maneuvers is shown in Figure 10
,
top, A, and bottom, B. Previous studies have
demonstrated that TLC does not change significantly during exercise,
and it is especially unlikely to change within a 10- to 20-s time
period necessary to perform the maneuvers.29
However,
whether or not this holds true in disease populations such as asthma
remains to be determined. Another potential source of error occurs when
subjects are asked to perform an IC or MFVL maneuver immediately prior
to the tidal loops obtained during exercise. Breathing pattern and
likely EELV will change transiently after this maneuver; therefore,
they should be performed after the tidal loops have been collected or
at least separated by an adequate time interval.5
8
14
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Figure 9. Unequal inspiratory and expiratory volumes may
occur because of electrical changes over time, to nonlinearities in the
flow or volume sensing device, as well as to physiologic changes
(temperature, humidity, gas density and viscosity, and turbulence).
Large differences in expiratory and inspiratory volumes make it
difficult to accurately place the tidal loops within the MVFL.
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Figure 10. Top, A: Example of "drift" in
volume over time. In this case, we note a consistent slope upward
indicating a larger expiration than inspiration. Two IC maneuvers can
be performed and volumes were aligned according to the ICs at TLC
(bottom, B). Another option is to change the slope of
the end expiratory lung volumes and reset to zero. However, this
assumes that the EELV is not changing within this time period.
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Placing the Tidal FV Loop Within the MFVL Envelope
The measurement of expiratory flow limitation, inspiratory flow
capacity, EILV, EELV, and ECAP are critically
dependent on placement of the extFVL within the maximal volitional FV
envelope. As noted previously, an IC maneuver can be performed to
correct for drift of the volume signal by aligning at the full
inflation lung volume (ie, TLC or VC); however, measurement
of ICs also provide an index of change in EELV (TLC/IC = EELV) in
order to place the extFVL within the MFVL. Changes in EELV have been
well studied in a number of populations during
exercise.5
6
7
8
29
Most studies have demonstrated an
intensity related fall in EELV in normal subjects of 0.5 to 1.0
L.8
14
27
However, with expiratory flow limitation, EELV
often rises, sometimes to levels above the resting
FRC.6
7
51
Thus, a precise estimate of this lung volume is
necessary, and a resting FRC cannot be used. If two IC maneuvers are
performed to correct for small differences in the inspiratory to
expiratory volumes (drift) and to place the tidal FV loops, an
important assumption is that EELV is not altered by performing the
maneuvers. Again, this could occur as subjects prepare to perform an IC
or transiently after the maneuver is performed. Thus, two IC maneuvers
should be separated by a substantial number of breaths to allow the
"true physiologic" EELV to be achieved, or several breaths should
be measured prior to the patient being asked to perform the maneuver.
Ideally, the patient is coached to perform the IC maneuver at the end
of a normal exhalation, EELV.
Previous studies have used direct measurements of EELV during exercise
by inert gas dilution techniques.27
52
The EELV obtained
in this manner agrees well with changes in IC in healthy populations,
but it may not be useful in patients with airway obstruction (secondary
to flow limitation, and airways with varying mechanical time constants
and ventilation maldistribution).27
Thus, in most cases,
the change in IC likely represents a better estimate of the change in
EELV with exercise if performed appropriately. Measurement of the EELV
directly requires an increased degree of equipment sophistication
relative to the IC maneuver and is not used in the majority of clinical
exercise laboratories.27
A potential source of error in the IC maneuver is that subjects may not
inspire fully to TLC. This would be particularly true in subjects with
muscle weakness or obesity where fatigue and a large inspiratory load
might play a role. Several studies have used an esophageal balloon to
measure maximal inspiratory pressures during the IC
maneuvers.8
14
21
23
27
29
If the maximal inspiratory
pressure obtained during exercise (with an open glottis) is similar to
that obtained repeatedly at full inflation (TLC) at rest, one is more
confident that TLC was reached during the maneuvers.5
6
29
Failure to achieve the pre-exercise target pressures would require
repeat IC maneuvers during exercise. End-expiratory esophageal pressure
has also been monitored in several studies as an index of change in
EELV prior to performing the IC maneuver.27
In the
majority of patients, it is likely that adequate IC maneuvers can be
performed (for placement of the FV loops) during exercise if sufficient
time is spent prior to exercise performing the
maneuvers.53
Defining the MFVL
MFVLs are plotted in association with the extFVLs to determine the
degree of ventilatory constraint. Most studies have demonstrated a
small bronchodilation early in exercise that may be exaggerated in
aging and in subjects with mild to moderate COPD.5
6
7
45
During prolonged exercise in asthmatics, there may be a slight decrease
in the MFVL after about 15 min.54
Thus, a pre-exercise
MFVL may underestimate or overestimate the capacity available during
exercise depending on the population. MFVLs may be difficult to perform
during exercise, especially in some disease populations. They have,
however, been performed successfully in normal subjects and
asthmatics,5
and in patients with mild to moderate COPD as
well as in patients with CHF.6
39
53
Previous studies have
suggested that in normals, the exercise-induced bronchodilation is
present for a short period of time immediately after exercise and,
thus, a postexercise MFVL may provide the simplest estimate of maximal
available flows and volume during exercise.36
In
asthmatics, the lability of airway tone may necessitate assessment of
the MFVL as close to the time of measuring the extFVLs as
possible.5
54
Maximal expiratory maneuvers resulting in excessive expiratory pleural
pressure generation have been shown to underestimate the true maximal
air flows at any given lung volume (< 70 to 80% of TLC) due to gas
compression in the chest.55
56
Thus, the true capacity for
airflow generation at a given volume may be underestimated,
particularly over the effort-independent portion of the MFVL. Although
not an established technique, the potential for underestimating maximal
available air flows may be circumvented by having subjects perform
a series of three to five expiratory maneuvers at different efforts
from TLC to RV and taking the highest flow obtained at each lung volume
(Figure 11 ).7
8
45
55
56
These various effort loops can be aligned at
TLC with the maximal effort loops and the expiratory boundary of the
maximal effort loops increased in accordance with any increased
expiratory flows noted with the submaximal efforts. MFVLs can also be
performed in a volume displacement plethysmograph where a separate flow
sensor compensates for the compression of gases when measured at the
mouth. The ideal MFVL for comparison to the exercise data is difficult
to determine, as the expiratory intrathoracic pressures produced during
heavy exercise tidal breathing may also cause gas compression in some
subjects. Thus, the maximal expiratory airflows obtained in a
plethysmograph may not truly be available in some flow-limited
subjects. For most subjects, the pre- or postexercise MFVL likely
represents an adequate assessment of the maximal available flow.
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Figure 11. Correction for gas compression to obtain the
maximal available expiratory flows: a series of expiratory maneuvers
from TLC to RV at different efforts can be performed and a line
extrapolated from the highest values obtained at each lung volume
during the maneuvers used as the maximal available expiratory flows.
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Limits to Defining Expiratory Flow Limitation and
ECAP
As previously noted, the assessment of expiratory flow limitation
and ECAP (as defined) is dependent on an adequate
assessment of MEFs and placement of the extFVL within the MFVL.
Whether or not the expiratory flow limitation described by the percent
of the tidal breath that meets or exceeds the MFVL represents
"true" flow limitation is controversial.10
39
Previous
studies that have examined the relationship of flow and transpulmonary
pressure (at a given lung volume) demonstrated that flow begins to
level off (pressure increasing out of proportion to flow) before a true
limit (increase in pressure without an increase in flow)
occurs.8
45
55
56
Thus, despite the difficulty in
defining the MEFs, the point where the tidal breath meets or exceeds
the expiratory boundary of the MFVL likely represents at least mild
flow limitation (a rising resistance to airflow) or "impending"
flow limitation. Recent use of a brief negative pressure during
expiration may more clearly define whether true expiratory flow
limitation occurs; however, using this technique, it is difficult to
quantify the percent of the breath that may be involved.10
The ECAP (as defined) also assumes an instantaneous
rise in flow at the onset of expiration. This is not typically observed
during exercise and would tend to slightly overestimate ventilation for
this reason.5
Additional algorithms may better define
physiologic change in flow on the onset of expiration.
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Acknowledgements
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The authors would like to thank Kathy O'Malley
and Sean M. Connery for technical assistance associated with several of
the studies reviewed in the manuscript. In addition we appreciate the
work of Audrey Schroeder in preparing the manuscript.
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Footnotes
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For editorial comment see page 277.
Abbreviations: CHF = congestive heart
failure; CPET = cardiopulmonary exercise testing;
EELV = end-expiratory lung volume; EILV = end-inspiratory lung
volume; extFVL = tidal exercise FV loop; FRC = functional residual
capacity; FV = flow-volume; IC = inspiratory capacity;
ILD = interstitial lung disease; MEF = maximal expiratory flow;
MFVL = maximal
TOP
Abstract
Introduction
