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Department of Medicine, Faculty of Medicine, University of Calgary, Calgary, Alberta, Canada T2N 4N1
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
ABSTRACT 
Isono, Shiroh, Thom R. Feroah, Eric A. Hajduk, Rollin Brant,
William A. Whitelaw, and John E. Remmers. Interaction of
cross-sectional area, driving pressure, and airflow of passive velopharynx. J. Appl. Physiol. 83(3):
851-859, 1997.
Previous studies have shown that, when the
pharyngeal muscles are relaxed, the velopharynx is a highly compliant
segment of the pharynx. Thus, under these circumstances,
cross-sectional area of the velopharynx (AVP), driving
pressure across the velopharynx (
P), and inspiratory airflow
(
I) will
be mutually interdependent variables. The purpose of the present
investigation was to describe the interrelation among these three
variables during inspiration. We studied 15 sleeping patients with
obstructive sleep apnea/hypopnea when the pharyngeal muscles were
rendered hypotonic by applying continuous positive airway pressure to
the nasal airway.
AVP, determined by endoscopic imaging, was significantly greater at onset of
I limitation
than at minimum oropharyngeal pressure
(P < 0.01). Snoring was never
observed during
I
limitation. In a subgroup of six patients, values for P,
I, and
AVP were obtained
at 0.1-s intervals at various levels of mask pressure. For these six
patients, the mathematical expression
I = 0.657(AVP/Amax) · P0.332,
where Amax is
maximal AVP,
described the relationship among the three variables
(R2 = 0.962) for
flow-limited and non-flow-limited inspirations. The impedance of the
passive velopharynx, defined as
P0.33/,
was inversely related to
AVP and increased
dramatically when AVP was <0.3
cm2. In summary, we observed a
progressive decrease in
AVP during flow-limited inspiration in patients with obstructive sleep apnea. This
constriction of the velopharynx contributes to an increase in
velopharyngeal impedance that, in turn, counterbalances the increase in
P during flow limitation.
obstructive sleep apnea; pharyngeal mechanics; fluid flow dynamics; flow limitation; dynamic collapse
INTRODUCTION WHEN THE PHARYNGEAL MUSCLES are relaxed, the pharynx of
patients with obstructive sleep apnea (OSA)/hypopnea is a highly
collapsible conduit (8). For inspiratory flow
( To simplify our investigation, we selected patients having only one
highly compliant segment, that being the velopharynx. To render the
pharyngeal muscles hypotonic, studies were performed while the patient
slept and received therapeutic levels of nasal continuous positive
airway pressure (CPAP). The genioglossus, and presumably other
pharyngeal muscles, exhibits little electrical activity under these
conditions (13). We have demonstrated that this hypotonia also exists
during diazepam-induced sleep and is maintained when the nasal airway
pressure is reduced for a single breath (Ref. 13 and unpublished
observations). To image the velopharyngeal lumen, we used
videoendoscopy and calculated the luminal cross-sectional area
(AVP).
MATERIALS AND METHODS
I) to occur
through the pharyngeal airway, supraglottic pressure must decrease as a
result of contraction of thoracic inspiratory muscles. As
I increases with increasing contraction of these muscles, pharyngeal luminal pressure decreases because of increase in kinetic energy at the segment
and dissipative energy loss at upstream resistances. If the pharynx is
hypotonic and, hence, highly compliant, the decrease in luminal
pressure will, in turn, decrease cross-sectional area of one or more of
its segments. Such narrowing further increases the kinetic energy of
gas flowing through the segment(s), thereby further decreasing luminal
pressure. In this way, a highly compliant pharyngeal segment may narrow
progressively during inspiration and, ultimately, may become a
"choke point" that limits airflow (16). Although
such flow limitation has been well described in patients with OSA (21)
and presumably results from such choke point behavior of the pharynx,
no observations are available of pharyngeal lumen during
I limitation.
We hypothesize that when inspiratory airflow is limited by the pharynx,
the cross-sectional area of the flow-limiting segment decreases
progressively as the downstream pressure decreases. The purpose of the
present investigation was to test this hypothesis and to describe the
dynamic pharyngeal mechanics for patients with OSA when the pharyngeal
muscles are hypotonic.
P), defined as Pnp 
Pop.
The catheters were perfused by a slow, bias flow of water. A fiberoptic
endoscope (PF-27L, 2.7-mm OD, Olympus) was inserted through the nose to
visualize the pharynx. A nasal CPAP mask was applied to the patient and
sealed to the skin by using a silicone rubber foam. Care was taken to
eliminate leaks. The nose mask was connected to a pressure
servocontroller through a pneumotachograph (Fleisch no. 1). The
pressure servocontroller regulated nasal airway pressure with negative
and positive blowers by using the mask pressure (Pm) as a feedback
signal. Pm was measured by using a differential transducer (MP-45,
Validyne). The polysomnographic data, pressure, and flow were recorded
on a 16-channel recorder (ES 1000, Gould). The fiberscope was connected
to a camera (WC-CD 50, Panasonic), and the image was displayed and
recorded on a videotape, along with a time code (T5010, Telcom
Research). The time code, together with simultaneously recorded values
of pressure and flow, was stored in a personal computer. This dual
recording of the time code allowed subsequent identification of
pressure and flow values corresponding to the simultaneously recorded
image.
The subject was allowed to fall asleep while lying supine, with the
neck in a neutral position, and the study was performed during
non-rapid-eye-movement sleep. In four cases, adequate data were
obtained during natural sleep. In 11 cases, such data were not obtained
because sleep was disrupted, and adequate sleep occurred only after
intravenous injection of midazolam (10-15 mg). Pm was set at a
level that fully distended the pharynx, as determined by progressively
increasing Pm until no further increase in
AVP was observed.
This pressure, referred to as holding pressure, was applied before and
after single-breath tests in which Pm was reduced abruptly for a single
breath at the end of inspiration from holding pressure to a
preselected, lower test pressure. Such single-breath tests were
repeated, using 5-10 different values of test pressure. The range
of test pressure included closing pressure (Pc), the pressure
associated with complete velopharyngeal closure at the end of test
expiration. If the subject was aroused during a single-breath test, the
data were discarded and the trial was repeated.
With the use of the protocol described above, the entire pharynx was
systematically evaluated in each patient. A series of single-breath
tests was first performed while the hypopharynx (tip of the epiglottis
to vocal cords), then the oropharynx (margin of soft palate to tip of
epiglottis), and then the nasopharynx (end of nasal septum to margin of
soft palate) were viewed. Each pharyngeal segment was classified as a
primary or secondary site of narrowing, according to previously
described criteria (13, 15). In all these cases, the site of
nasopharyngeal closure was restricted to the velopharynx, the segment
of the nasopharynx bounded ventrally by the soft palate.
The videotaped images corresponding to selected times (see
Data analysis) were
digitized (data translation DT2803, Frame Grabber). AVP in each image
was measured by using cursor-controlled software, and the absolute
value for AVP was
calculated by reference to the diameter of the pressure catheter (1.7 or 2.0 mm) where it passed through the lumen of the constricting
segment.
Accuracy of the pressure and
AVP
measurements.
Response characteristics of the pressure measurement with the
fluid-filled catheter were carefully evaluated by using a rigid container (25 liters) with a loudspeaker mounted in the wall. The
speaker was driven by a sine wave to create a pressure wave in the
container. Responses of the fluid-filled pressure catheter-transducer system with the bias-flow running water were compared with that of a
high-frequency air-filled transducer (MP-45, Validyne).
The amplitude of the pressure wave recorded by the fluid-filled
catheter stayed constant ±5% up to 13 Hz. The time delay due to
phase shift between fluid-filled catheter system and air-filled
transducer was <0.025 s up to 13 Hz. Sudden rupture of elastic
membrane covering a rigid container was used to provide a square-wave
pressure signal. A 90-10% and 10-90% response to ±10
cmH2O square pressure signal was
reached within 0.055 s.
Accuracy of the measurement of the
AVP was validated
by using various tubes of known cross-sectional area (range;
0.12-1.77 cm2) and was
found to be accurate within 10%.
Data analysis.
As we previously reported, static velopharyngeal
pressure/area relationships for each of the six subgroup patients was
described by the exponential equation
|
(1) |
AVP).
For each single-breath test having Pm greater than Pc, we examined the
relation between
I and P.
When no increase in airflow was observed, despite increasing P, the
inspiration was classified as flow limited. Conversely, when positive
dependence of
I on P
was observed, throughout the test inspiration, the inspiration was
classified as non-flow-limited inspiration.
The mechanical behavior of the velopharynx during flow-limited
inspiration was evaluated in four to five single-breath tests (mean = 4.5) in each of the 15 patients. Values of P and
AVP were obtained
at the beginning of inspiration, and values of
I, P, and
AVP were measured
at the onset of flow limitation and at the nadir of Pop. A more
detailed analysis of the behavior of the velopharynx was performed in a
subgroup of six patients (patients
1-6). In these six patients, referred to as
subgroup patients, values for P,
I, and
AVP were
collected every 0.1 s throughout inspiration for flow-limited and
non-flow-limited inspirations. Resistance of the nose (Rn) and the
velopharynx (Rvp) were calculated as the ratio of the driving pressure
for each segment (Pm/Pnp or Pnp/Pop) to the simultaneously observed airflow.
Data derived from the subgroup of six patients were fitted with the
following equation
|
(2) |
I increases as P increases for a constant geometry;
2) large
I is
obtained by a constant P as
AVP increases;
and 3) during flow limitation, increase in P is balanced by simultaneous reduction of
AVP. Individual patient data and group data were fitted to the equation by using a
nonlinear, least-squares method (NONLIN SYSTAT, 1985). Because the
values of a and
b were nearly equal to unity and 0.33, respectively, we defined a variable impedance (Z) of the velopharynx,
as follows
|
(3) |
P-I
relationship for a constant
AVP. Therefore, Z
reflects the resistive characteristics of the velopharynx when the air
flows through it due to introduction of P and can be interpreted as physiological Z for the air to flow through the collapsible velopharynx.
Mean kinetic energy of the air at the velopharynx (Pke) was calculated
from the equation Pke = 
where 
is a density of the air (1.3 kg/m3) and
, the average velocity of the air
through the velopharynx, was calculated from the ratio
I/AVP.
All values were expressed as means ± SD. Statistical analysis was
performed by using analysis of variance and Tukey's test. P < 0.05 was considered to be
significant.
RESULTS
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I,
AVP, P, Pop,
Pke, Rn,
RVP, and Z for each
of these three times for each of the 15 patients. Mean
I was greater at onset of flow limitation than at minimum Pop
(P < 0.05). Compared with the value
at beginning of inspiration, the mean value of AVP was 30% less
at the onset of flow limitation (P < 0.05) and 66% less at the nadir in Pop
(P < 0.01). Mean values of Pke
increased significantly from onset of flow limitation to minimum Pop
(P < 0.01). Mean values of
RVP and Z
increased significantly during flow limitation, whereas
Rn showed no
change. Figure 1 illustrates dependence of
I and
AVP at onset of
flow limitation on Pm for each of 15 patients. For each patient,
I and
AVP at onset of flow limitation increased as Pm increased.
|
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I;
A) and cross-sectional area of
velopharynx (AVP;
B) at onset of inspiratory flow limitation (IFL) on mask pressure (Pm) for each of 15 patients. Different symbols represent different subjects.
Subgroup analysis of flow-limited and non-flow-limited inspirations. The dynamic behavior of the velopharynx during flow-limited and non-flow-limited inspirations was studied in 49 single-breath tests (34 flow-limited tests; 15 non-flow-limited tests) in the six subgroup patients (patients 1-6), where values of
I,
AVP and P were
obtained at 0.1-s intervals. Figure 2
illustrates for one patient (patient
5) the typical time courses of
I, P, AVP, Pke, and
RVP at four
different values of Pm. The far left column provides an example of an inspiration without flow
limitation (Pm = 6 cmH2O).
I
progressively increased during inspiration as a result of a progressive
increase in P so that
RVP remained at a
low and constant value. Cross-sectional area decreased only slightly
and, therefore, Pke changed little. By contrast, when Pm was somewhat
lower (Pm = 1 cmH2O), inspiratory airflow was limited (Fig. 2, second column from
left). During this flow-limited inspiration,
I remained
relatively constant, while P increased slightly,
AVP progressively
decreased, and Pke continuously increased. These changes in
AVP, P, and
Pke became more prominent at lower values of Pm (Fig. 2,
right two columns). In addition, at
the lowest value of Pm (Pm = 1
cmH2O) (Fig. 2,
far right column) RVP increases
dramatically during flow limitation, whereas
I decreases
progressively.
I),
pressure difference (P) across the velopharynx [P = nasopharyngeal pressure (Pnp) oropharyngial pressure
(Pop)],
AVP,
velopharyngeal resistance (RVP),
and kinetic energy at the velopharynx (Pke) were obtained at 0.1-s
intervals from beginning of inspiration until Pop reached its minimum
value. Arrows indicate onset of flow limitation.
The data for all 49 inspirations for each of the six patients were fitted by Eq. 2, and Table 3 provides the results of this curve-fitting procedure for each patient. R2 values ranged from 0.744 to 0.906 with a mean R2 for the group equal to 0.855. Positive values of the constants a and b indicate that independent increases in AVP and
P
were associated with increases in
I. The
relationships between
AVP, P, and
I during
flow-limited and non-flow-limited inspirations can be graphically
displayed on a three-dimensional plot. Figure 3 illustrates a typical plot in one patient
(patient 1) for eight test
inspirations. Each thick line represents an iso-Pm curve, i.e., the
locus of simultaneously observed values of the three variables during
inspiration at a single value of Pm. The upper grid surface formed by
continuous lines graphically illustrates the regression
|
(4) |
P contour lines on this surface show that I increases
monotonically with increasing values of
AVP for any
constant P. Similarly,
I increases as
P increases for any constant
AVP as
demonstrated by the
iso-AVP contour
lines. Experimentally observed iso-Pm contour lines for this patient are located near or on the surface. Each iso-Pm line crosses the iso-AVP and iso-P guidelines, indicating that
AVP decreases and P increases during inspiration.
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P and
I for several
values of Pm in patient 1. Each solid
thick line represents simultaneously observed values of these variables
during inspiration at single Pm. Families of
iso-AVP and iso-P contour lines (thin lines)
form a grid on a surface which displays as a mathematical function (see
Eq. 4 in
RESULTS;
R2 = 0.853).
The results for all 49 inspirations in all six patients can be graphically summarized after normalizing AVP to Amax, as shown in Fig. 4. In Fig. 4A, each line represents simultaneous values of
I,
P, and
AVP/Amax
during inspiration at a constant value of Pm. Each iso-Pm curve
provides the observed points for a single test inspiration. An
inspiration beginning from a high value of AVP/Amax
(i.e., relatively high Pm) ascends a steep curve such that
I increases
with little change in
AVP/Amax
or P. By contrast, an inspiration beginning from a low
AVP/Amax
(i.e., relatively low Pm) ascends on the surface less steeply (i.e.,
P and
AVP/Amax change greatly for a unit increase in
I). This
trajectory becomes progressively flatter, and then
I actually
declines as P increases and
AVP/Amax
decreases. The upper grid (continuous lines) shown in Fig.
4B was generated by fitting
Eq. 2 to all data for all six
patients, yielding the following relationship
|
(5) |
P, I, and
AVP is a
two-dimensional plot of P vs.
I, as shown in
Fig. 5 for each of the six patients. The solid lines provide iso-Pm data that are superimposed on a family of
AVP isopleths
(dotted lines) derived from the above equation. This figure illustrates
that during flow limitation, P increases progressively and
AVP decreases
dramatically in all cases.
P, and I
during 49 inspirations (15 non-flow-limited and 34 flow-limited
respirations) from 6 patients. Each solid line represents data from
single inspiration at a constant Pm.
B: common surface
fitted to data as Eq. 5 (see RESULTS;
R2 value = 0.962).
P-I curves
with family of iso-AVP lines for each of 6 patients. Solid lines,
P-I
relationships in spontaneous inspiration for variety of fixed Pm. Any
combination of P and
I has
corresponding AVP value, as represented by a family of iso-AVP lines (dotted lines) on the
plane according to fitted mathematical function for each
patient.
The Z of the velopharynx was found to vary inversely with AVP. Figure 6 provides all values of Z for all six patients, plotted as a function of simultaneously observed values of AVP. The data are fitted by the relationship Z = 0.457/
.
Figure 6A plots Z on a linear scale,
and Fig. 6B plots Z on a log scale.
The data for all patients at all Pm values scatter along a single
inverse relationship, showing that Z depends critically on the absolute value of AVP. The
linear plot (Fig. 6A) shows that,
for values of AVP
in the range of 0-0.3 cm2,
small reductions in
AVP result in
dramatic increases in Z. The logarithmic plot (Fig.
6B) reveals that the inverse
relationship between Z and
AVP obtains for
low values of Z, i.e., Z <10
cmH2O · l
1 · s.
P0.33/I.
B: Logarithmic transformation of
ordinate shows that Z depends on
AVP even at large
values of AVP.
Curve passing through data points is calculated from Z = K/AVP,
where K = 0.457 (see Table 3).
DISCUSSION
The present study provides the first systematic
observations of luminal
AVP under dynamic
conditions. The results reveal that the interdependence of
I, P, and
AVP for all
patients is well described by Eq. 5, a
relatively simple equation,
(R2 = 0.962)
regardless of flow regimes, i.e., flow-limited and non-flow-limited inspirations. This relation signifies that
I depends
independently on relative area and on P, and the former dependency
is greater than the latter. During all inspirations, the velopharynx
progressively narrowed and P increased. Accordingly,
I was
determined by the balance between
AVP and P.
Specifically, continuous reduction of
AVP
counterbalanced simultaneous increase in P, resulting in constant or
decreasing I
(negative effort dependence) during IFL. The Z of the velopharynx
depended critically on
AVP, and a single
relationship (Z = 0.457/AVP)
described the inverse dependence of Z on
AVP for values of
Pm in all patients. Increments in Z associated with progressive
decreases in AVP
were at least one of the factors causing an increase in P during
IFL.
We studied patients while nasal CPAP was applied during sleep, which profoundly diminishes activation of the genioglossus (25). Furthermore, we have previously shown that this hypotonia is maintained for a single breath after an abrupt reduction of nasal CPAP (13), indicating that a single-breath test such as used here constitutes a useful method for investigating the mechanical properties of the hypotonic pharynx under dynamic conditions.
At the beginning of inspiration, contraction of inspiratory pump
muscles reduces Pop, which causes airflow through the collapsible velopharynx. As
I increases,
Pil decreases as a consequence of the increase in kinetic
energy of the air (Bernoulli effect) and as a result of upstream
dissipative energy loss, particularly in the nasal airway. The decrease
in Pil reduces
AVP in accordance with its dynamic compliance, and this narrowing of the velopharynx further increases kinetic energy of gas flowing through the
segment. The outcome of these causally interrelated
events depends on the intrinsic mechanical properties of the pharynx,
i.e., tube law of the pharynx, the initial area determined by the
upstream pressure and the downstream pressure. If the
pharyngeal wall is relatively stiff,
AVP will decrease
little during inspiration, and
I will increase continuously as downstream pressure falls, owing to
contraction of thoracic inspiratory muscles. This is the case for the
hypotonic pharynx when Pil exceeds Pc by >5
cmH2O. However, the
cross-sectional area of a more compliant velopharynx will decrease
during inspiration, such as when Pil is 1-5
cmH2O above Pc, thereby increasing
Z and lessening the increase in
I.
Because the caudal margin of the soft palate constitutes a structural
discontinuity and because the nasopharynx is more compliant than the
oropharynx, the nasopharynx assumes a funnel shape during inspiration,
being most narrow at its caudal margin. The cross-sectional area
increases abruptly at the junction of the velopharynx with the
oropharynx. Airflow in such an expansion tends to display jet flow and
flow separation (16). This can lead to dissipative energy loss in the
oropharynx and a reduction in Pop. Such behavior might account for the
observation that
I varies
linearly with P0.33 rather than
with P0.5, as would be expected
from the Bernoulli theorem. Accordingly, a greater P is necessary to
produce a given change in flow when this aerodynamics operates. In
addition, these flow dynamic changes also account for the steep slope
of the relationship between
AVP and Z at the
lower range of
AVP.
A three-dimensional plot of
AVP, P, and
I produces a
surface that describes the relationships over a wide variety of flow regimes. With the use of a collapsible tube placed in a rigid chamber,
P-I
relationships were demonstrated to depend on experimental conditions,
which were given by a combination of upstream pressure, downstream
pressure, and chamber pressure (3, 5-7, 12, 20). Rodbard (20) and
Holt (6, 7) found that when upstream pressure was maintained constant
above chamber pressure,
I at first
increased but then reached a constant value as downstream pressure
decreased. Holt noted that, during flow limitation, the tube changed
its geometry from fully open to partially collapsed; these observations
are compatible with ours. We observed that at low values of Pm, when
collapsibility is high,
I decreased as
P increased during IFL. This phenomenon is often referred to as
"negative effort dependence" (14). Jones et al.
(10) examined effects of alteration of the collapsibility of the
trachea on
P-I curves.
They found that increase in collapsibility led to decreasing maximum
flow through the trachea with increasing P (negative effort
dependence) while
I
progressively increased without flow limitation in rigid trachea.
The "waterfall" analogy, proposed by Permutt et al. (17) and
Permutt and Riley (18) and applied to upper airway by Schwartz et
al. (22) and Smith et al. (24), successfully accounts
for P-I
relationships in a Starling resistor model. The analogy elegantly
explains the linear relationship between upstream pressure and the
value of flow at the onset of IFL in sleeping normal subjects (22) and
in patients with OSA (24). The results of the present study (Fig. 1)
confirm these observations in patients with OSA under conditions of
reduced activity of the pharyngeal musculature. We observed that
I increased
with increasing upstream pressure in association with a corresponding
increase in cross-sectional area of the flow-limiting segment. The
waterfall analogy makes no predictions regarding the area of the
flow-limiting segment. Rather, the analogy summarizes events by
postulating a discontinuity in convective flow, i.e., a waterfall, so
that the height of the waterfall does not influence flow rate of the
waterfall. However, changes in cross-sectional area at the
flow-limiting segment are likely to be significant determinants of
I during flow
limitation. Jones et al. (11) thoroughly examined a
role of geometry of a collapsible tube in determining
I in excised
canine trachea. They found that cross-sectional area at the
flow-limiting segment was a significant determinant during flow
limitation and that cross-sectional area decreased with increasing P
whereas I remained unchanged. Our results are in agreement with
findings of Jones et al. and suggest that the flow
observed when flow is limited by the velopharynx is determined by a
balance between increase in P and decrease in
AVP.
Our results reveal that snoring and IFL are not necessarily linked mechanical phenomena. We frequently observed the latter but never the former. One possible reason for our failure to observe snoring is that the pharynx was hypotonic during these experiments. The lack of genioglossus activity means that the soft palate and the tongue form a continuous wall of the pharynx. Perhaps snoring cannot occur under these circumstances because of the high mass of the wall. By contrast, when the genioglossus is highly active, the base of the tongue is moved ventrally and a discontinuity occurs between the soft palate and the tongue. This would substantially decrease the mass of the velopharynx and allow the high-frequency oscillation of the soft palate characteristic of snoring.
In summary, a simple mathematical function (Eq. 2) described mutual interrelationships of
AVP, P, and
I during
inspiration over a variety of flow regimes in the passive pharynx of
sleeping OSA patients with a collapsible segment only at the
velopharynx. During flow-limited inspirations, the velopharynx
progressively narrowed and Pke increased. Simultaneously, the Z of the
velopharynx increased, consequent to a progressive reduction in
AVP, which offsets the simultaneous increase in P, leading to constant or decreasing I.
ACKNOWLEDGEMENTS
Present address of S. Isono: Dept. of Anesthesiology, Chiba Univ. School of Medicine, 1-8-1 Inohana, Chuo-ku, Chiba City, 260 Japan. Present address of T. R. Feroah: Depts. of Pediatrics and Physiology, Medical College of Wisconsin, 8701 Watertown Plank Rd., Milwaukee, WI 53226-0509.
FOOTNOTES
Address for reprint requests: J. E. Remmers, Dept. of Medicine, Faculty of Medicine, Univ. of Calgary, 3330 Hospital Drive N. W., Calgary, Alberta, Canada T2N 4N1.
Received 17 September 1996; accepted in final form 29 April 1997.
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