Vol. 93, Issue 3, 1084-1092, September 2002
A mathematical model to detect inspiratory flow limitation
during sleep
Khaled F.
Mansour,
James A.
Rowley,
A. A.
Meshenish,
Mahdi A.
Shkoukani, and
M. Safwan
Badr
Sleep Research Laboratory, John D. Dingell Veterans Affairs
Medical Center, Division of Pulmonary, Critical Care and Sleep
Medicine, Wayne State University, Detroit, Michigan 48201
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ABSTRACT |
The physiological significance of
inspiratory flow limitation (IFL) has recently been recognized, but
methods of detecting IFL can be subjective. We sought to develop a
mathematical model of the upper airway pressure-flow relationship that
would objectively detect flow limitation. We present a theoretical
discussion that predicts that a polynomial function [F(P) = AP3 + BP2 + CP + D, where F(P) is flow and
P is supraglottic pressure] best characterizes the pressure-flow
relationship and allows for the objective detection of IFL. In
protocol 1, step 1, we performed curve-fitting of
the pressure-flow relationship of 20 breaths to 5 mathematical
functions and found that highest correlation coefficients
(R2) for quadratic (0.88 ± 0.10) and
polynomial (0.91 ± 0.05; P < 0.05 for both
compared with the other functions) functions. In step 2, we
performed error-fit calculations on 50 breaths by comparing the
quadratic and polynomial functions and found that the error fit was
lowest for the polynomial function (3.3 ± 0.06 vs. 21.1 ± 19.0%; P < 0.001). In protocol 2, we
performed sensitivity/specificity analysis on two sets of breaths (50 and 544 breaths) by comparing the mathematical determination of IFL to
manual determination. Mathematical determination of IFL had high
sensitivity and specificity and a positive predictive value (>99% for
each). We conclude that a polynomial function can be used to predict
the relationship between pressure and flow in the upper airway and
objectively determine the presence of IFL.
upper airway; polynomial equation; pressure-flow relationship
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INTRODUCTION |
SLEEP-DISORDERED
BREATHING (SDB) can manifest as a spectrum from inspiratory flow
limitation (IFL) to hypopneas and apneas. Although clinicians and
investigators have long recognized the clinical importance of apneas
and hypopneas, the importance of IFL in the spectrum of SDB has only
recently been recognized with the recognition of the upper airway
resistance syndrome (UARS) (5). UARS is characterized by
repetitive episodes of IFL and decreases in esophageal pressure leading
to recurrent arousals (8). The repetitive flow-limitation
events have been associated with excessive daytime sleepiness
(5) and changes in blood pressure (6), which
are clinical and physiological responses that have also been noted with
apneas and hypopneas. In addition, our research laboratory has shown
that the presence of IFL in otherwise apparently normal subjects can
predict different responses to mechanical and chemical interventions
during sleep (2, 4).
The increasing clinical and physiological significance to the presence
of IFL necessitates that there be an objective and reproducible method
to detect IFL. Investigators have shown that flow-limitation events can
be detected without esophageal manometry (1, 7), but the
detection of flow-limitation in these studies is based on visual
inspection of the flow contour only, increasing the potential for a
subjective interpretation of the data. In studies from our laboratory,
we have determined whether a breath demonstrates IFL by either visual
analysis (2) or manual analysis of the pressure-flow loop
(Fig. 1; see METHODS for
definitions) (4, 17). Manual analysis of the pressure-flow
loop is a time-consuming task, and, despite a clear definition of IFL,
we have found there to be frequent interscorer differences in
determining whether a breath demonstrates IFL and that some breaths are
not easily characterized as either IFL or noninspiratory flow limited
(NIFL). We hypothesized that a mathematical model may provide a method for the objective detection of IFL. Previous investigators have shown
that the pressure-flow relationship of the upper airway can be modeled
mathematically (9, 16, 20), but these investigators did
not specifically develop a model to detect flow limitation. Therefore,
the objective of the work presented in this paper was to develop a
mathematical model of the pressure-flow relationship in the upper
airway that would detect flow limitation with precision, objectivity,
and reproducibility.
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Fig. 1.
Pressure-flow loops illustrating a nonflow limited (NIFL)
and a flow-limited (IFL) breath. A breath was labeled IFL if there was
a  1 cmH2O decrease in supraglottic pressure
(PSG) without any corresponding increase in flow ( )
during inspiration.
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Theory and Hypothetical Considerations
We consider a steady homogenous flow in a circular cylinder (the
upper airway), with the assumption that the flow of air in the upper
airway will expand without the loss or gain of heat. Consider a
streamline of air that connects two points M1,
the upstream pressure, which is atmospheric pressure in our model, and
M2, the downstream pressure, which is equivalent
to supraglottic pressure in our model. For each point, there is a
density (
), pressure (P), area (A), velocity
(V), and flow (F) that characterizes that point. In the
modeling that follows, it should be noted that the goal is
determination of the flow of the upper airway at the downstream
pressure point, M2. Flow, which is constant
throughout the upper airway, is given by
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(1)
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Solving for V1
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(2)
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where
The Bernoulli or energy equation for homogenous fluid such as air,
on one streamline, through M1,
M2, and neglecting the effect of gravity is
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(3)
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Because air is a compressible, we need to consider the heat
kinematic ratio 
/( 
1). If we set the kinematic heat ratio as K = /( 1), then we can rewrite
Eq. 3 as
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(4)
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Because the path of the upper airway is short, we may assume
1 
2 = . We can then rearrange
Eq. 4 as
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(5)
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Substituting V
from
Eq. 2
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(6)
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Solving for V
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(7)
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Squaring both sides of Eq. 1, we can obtain the flow
squared at point M2
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(8)
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Substituting for V from
Eq. 7
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(9)
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Rearranging
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(10)
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By taking the square root of both sides of Eq. 10, we
obtain
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(11)
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Let
Therefore, flow through a streamline between two points,
M1 and M2, is given by
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(12)
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With the use of Newton's expansion law
we obtain
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(13)
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If we let
we can then substitute these coefficients into Eq. 13
to get a polynomial function that approximates flow [F(P)] in
terms of the supraglottic pressure. For this function, we assume that P1 is atmospheric pressure, which is a constant, and
P2 = P, which we now define as the supraglottic
pressure
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(14)
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Per Newton's expansion law, the relationship between pressure and
flow could also be predicted by a quadratic equation
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(15)
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However, the nature of a polynomial function predicts that a
polynomial function would be expected to better estimate the pressure-flow relationship than the quadratic function for flow-limited breaths. This is because, for IFL breaths, the polynomial function is
characterized by two deflections, as illustrated in Fig.
2. A two-deflection relationship will
better approximate the measured pressure-flow relationship of IFL
breaths, which are characterized by a point of maximum flow, followed
by a decrease and plateau in flow (Fig. 1). The quadratic function,
however, is characterized by only one deflection (see Fig. 2) and,
therefore, does not as closely approximate the measured pressure-flow
relationship of IFL breaths.
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Fig. 2.
Graphical representation of the mathematical nature of polynomial
(left) and quadratic (right) functions. The
polynomial function is characterized by two deflections (Max and Min),
whereas the quadratic function is characterized by one deflection
(Max).
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While performing the initial curve-fitting analysis (see
METHODS), we noted that the nature of the polynomial
function, in contrast to the quadratic function, would allow for the
objective differentiation of IFL and NIFL breaths. In particular, we
noted that for the polynomial function, the maximal flow of the
predicted relationship usually was at the same pressure as the measured maximal flow. In contrast, the predicted maximal flow for the quadratic
function would be at a more negative pressure. To objectify these
observations, we hypothesized that we could determine the presence of
flow limitation by examining a derivative of the polynomial function,
which is represented by the slope of the pressure-flow relationship.
The derivative of the polynomial function is
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(16)
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Theoretically, for NIFL breaths, flow would continue to increase
beyond the point of maximal flow if there were further decreases in
supraglottic pressure. Therefore, the derivative of the polynomial function (or the slope of the pressure-flow curve) at the actual maximal flow is negative. This is illustrated in Fig.
3A, which shows a NIFL breath
(solid line) and the theoretical relationship by using the polynomial
function (dashed line). At the measured maximal flow, the slope of the
theoretical pressure-flow relationship is negative, as illustrated in
Fig. 3B. However, for breaths that demonstrate IFL, there
are no further increases in flow despite decreasing supraglottic
pressure (Fig. 3C). Therefore, the slope or derivative of
the polynomial function at the measured maximal flow is either zero or
positive for flow-limited breaths (Fig. 3D). Therefore, at
maximal flow, two cases can be determined from Eq. 15. If
1) df/dP < 0, the breath is NIFL; and 2)
dF/dP < 0 or dF/dP = 0, the breath is IFL.
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Fig. 3.
Graphical representation of the theoretic considerations regarding
the ability of the polynomial and quadratic functions to distinguish
between NIFL (A and B) and IFL breaths
(C and D). The vertical straight line in all
panels is at the measured maximal flow. A and C:
measured pressure-flow relationship (solid line) and the theoretical
polynomial (dashed line) and quadratic (dash-dot line) relationships.
B and D: slopes of the predicted functions at
increasing PSG values. The slope at the measured maximal
flow for both the polynomial ( ) and quadratic functions
( ) remains negative for NIFL breaths (B).
The slope of the polynomial function at measured maximal flow becomes
positive for IFL breaths, whereas the slope of the quadratic function
remains negative (D).
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By a similar analysis, we hypothesized that the derivative of the
quadratic function cannot be used to determine whether the pressure-flow relationship demonstrates flow limitation. The derivative of the quadratic function is given as
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(17)
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However, if the quadratic function is used to characterize the
pressure-flow relationship (dashed lines in Fig. 3, A and C), the derivative of the quadratic function cannot be used
to distinguish between nonflow-limited and flow-limited breaths. This
is illustrated in Fig. 3, B and D, which shows
that the derivative of the quadratic equation will be negative for both
types of breaths. In other words, dF/dP < 0 for all breaths.
In summary, theoretical considerations indicate that the
relationship between flow and supraglottic pressure in the upper airway
can be characterized by either a quadratic or polynomial function.
However, on the basis of theoretical considerations, we hypothesized
that the polynomial function was the better of the two functions to
mathematically model the upper airway because it would provide the best
fit compared with the actual pressure-flow relationship, and use of its
derivative would provide an objective and accurate method for the
detection of IFL.
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METHODS |
Measurements and Manual Determination of Flow
Limitation
For each breath, airflow was measured by a pneumotachometer
(model 3700A, Hans Rudolph) attached to a nasal mask. Supraglottic airway pressures were measured by using a pressure-tipped catheter (model TC-500XG, Millar) threaded though the mask and positioned in the
oropharynx just below the base of the tongue. Correct placement in the
hypopharynx was confirmed by advancing the catheter tip for 2 cm after
it disappeared behind the tongue.
The sequence of analysis is illustrated in Fig.
4. During the studies, airflow and
supraglottic pressure were recorded simultaneously with Biobench data
acquisition software (National Instruments, Austin, TX) on a separate
computer (Fig. 4A). For each breath, the onset of
inspiration was defined as the sampling point at which inspiratory
flow = 0. On the rare occurrence in which there was a shift in
baseline, the nadir flow was determined and the flow values shifted
appropriately. Because the Millar catheter provides relative pressures,
supraglottic pressure was set to zero for the inspiration onset
sampling point and the remaining values for the breath were calculated.
A pressure-flow loop was generated (Fig. 4B), and the loop
was analyzed for the presence of IFL (Fig. 1). A breath was labeled IFL
if there was a 1 cmH2O decrease in supraglottic pressure
without any corresponding increase in flow during inspiration. If the
flow-pressure relationship did not meet this criterion, the breath was
labeled as NIFL.
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Fig. 4.
Sequence of data analysis. A: example of 3 breaths from
the raw tracing from a polygraph. The data analysis was performed on
the middle (boxed) breath. B: pressure-flow loop of the
indicated breath. The selected breath demonstrates flow limitation
because there is no increase in flow despite a >1 cmH2O
decrease in PSG. C: curve-fitting analysis shows
only the ascending limb of the inspiratory portion of the pressure-flow
loop (solid line) and the fitted polynomial curve (dashed line).
The equation for the fitted curve is F(P) = 0.0005P3 0.0151P2 0.1137P + 0.0338. D: determination of flow limitation
shows the plot of the slope of the polynomial function vs.
PSG. For this breath, slope = 0.0015P2 0.0302P 0.1137. Because the
slope of the polynomial function is 0.001 (0) at measured maximal
flow (vertical line), the breath is characterized as IFL by the model.
EEG, electroencephalogram; SaO2, arterial oxygen
saturation.
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All analyzed breaths in the following protocols were obtained during
stage 2 non-rapid eye movement sleep. Breaths from
wakefulness were not analyzed as IFL is not observed during
wakefulness. As slow wave and rapid eye movement sleep are uncommonly
observed in the heavily instrumented subjects, breaths from these
stages could not be analyzed. In addition, only breaths free from
artifact were included in the analysis. All breaths were obtained from healthy adults with no sleep-related complaints who had volunteered for
research studies in the laboratory. All subjects were free of SDB, as
measured by apneas and hypopneas, on baseline polysomnography. Demographics of the subjects are presented within each protocol.
Protocol 1: Does the Polynomial Function Best Predict the
Relationship Between Pressure and Flow in the Upper Airway?
Step 1: curve fitting.
To model the upper airway mathematically, we performed a curve-fitting
analysis with Sigma Stat 2.0 software (Figs. 4C and 5A). The purpose of this
analysis was to determine which of five regression equations (Table
1) best estimated inspiratory flow (the
dependent variable) as a function of supraglottic pressure (the
independent variable). This process is similar to performing a linear
regression, in which the predicted relationship can be given by the
equation: F(P) = AP + B. However,
because the pressure-flow relationship is not linear, we used five
nonlinear regression functions. The first two are derived from the
theoretical considerations above: quadratic and polynomial. The third,
a single-term hyperbolic, has previously been proposed as an accurate
predictor of the pressure-flow relationship (9). In
addition, we analyzed two additional functions: double-term hyperbolic
and exponential (13). Neither pressure nor flow values
were transformed before the curve fitting (14). This
analysis was performed on 20 breaths (10 NIFL, 10 IFL) derived from
four subjects [1 man, 3 women, mean age 22 ± 3 yr, mean body mass index (BMI) 23.0 ± 3.0 kg/m2]. For each
calculated function, we determined the coefficient of determination
(R2), which indicates how much of the
variability in one variable (flow) is explained by knowing the value of
the other (supraglottic pressure) (12).
R2 for IFL and NIFL breaths were compared
between the five functions by using one-way repeated-measures ANOVA,
with breath number as the repeated measure and the function as the
factor for comparison. If there was a significant difference between
the groups, a Student-Newman-Keuls test was performed to detect
between-group differences, with P < 0.05 set as the
level for a significant test. The same test was performed on the
combined groups of breaths.
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Fig. 5.
Illustrations of the analyses done in protocol 1. A: example of curve fitting that shows the actual data
points ( ) and the predicted pressure-flow
relationships if the points are fitted to a quadratic function (solid
line) or the 2-term hyperbolic function (dashed line). B:
example of error fit that shows the actual (solid line) and predicted
(dashed line) pressure-flow relationships. The predicted relationship
uses the quadratic function. The shaded area is the graphical
representation of the mathematical formula for error fit given in the
text.
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Step 2: error fit.
To determine the degree of approximation between the pressure-flow
relationship derived from either the quadratic or polynomial function
to the actual pressure-flow relationship, we determined the error fit
for 50 breaths, 25 each NIFL and IFL derived from 8 subjects (5 men, 3 women, mean age 25 ± 4 yr, mean BMI 26.2 ± 4.8 kg/m2). Only the quadratic and polynomial functions were
studied on the basis of the results of the curve-fitting analysis (see
RESULTS). An illustration of the concept of error fit is
given in Fig. 5. The right shows the actual pressure-flow
relationship for an IFL breath (solid line) and the predicted
pressure-flow relationship by using the quadratic function (dashed
line). The gray areas show the difference between the two
relationships. The smaller the gray area, the smaller the error fit and
the more closely the predicted relationship approximates the actual
pressure-flow relationship. The error fit is a mathematical
representation of this gray area. Mathematically, error fit is defined
as
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(18)
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where 
is the
summation of a series of points, yk represents
the points in the original function, and yi
represents the points in the fitted function (14). By
using this formula, as the predicted pressure-flow relationship more
closely approximates the actual relationship, the error fit or
difference between the two relationships decreases. The error fit for
IFL and NIFL breaths were compared between the two functions by using
one-way repeated-measures ANOVA, with breath number as the repeated
measure and the function as the factor for comparison. If there was a
significant difference between the groups, a Student-Newman-Keuls test
was performed to detect between-group differences with
P < 0.05 set as the level for a significant test. The
same test was performed on the combined groups of breaths.
Protocol 2: Does the Polynomial Function Objectively Detect Flow
Limitation?
Step 1.
By using the same 50 breaths with which we determined the error fit, we
determined the slope of the polynomial function at the measured maximal
flow for the polynomial equation (Fig. 4D). Per the
hypothesis, if the slope at the measured maximal flow was <0, we
labeled the breath NIFL; if the slope at the measured maximal flow was
0, we labeled the breath IFL. We calculated the sensitivity,
specificity, positive predictive value (PPV) and negative predictive
value (NPV) for the detection of IFL breaths by the polynomial model
compared with the standard method (described at the beginning of
METHODS) with the use of standard formulas (18).
To confirm the hypothesis that the slope at the measured maximal flow
for the quadratic equation would be negative for both IFL and NIFL
breaths, we determined the slope at the measured maximal flow for the
same 50 breaths. We report the proportion of NIFL and IFL breaths with
a negative slope.
Step 2.
To validate the results, we then determined the slope of the polynomial
function at the measured maximal flow by using the polynomial equation
for 544 randomly selected breaths from 20 subjects without SDB as
measured by apneas and hypopneas (10 men, 10 women, mean age 30 ± 8 yr, mean BMI 25.2 ± 4.3 kg/m2). Applying the
hypothesis, we labeled each breath as NIFL or IFL. We calculated the
sensitivity, specificity, PPV, and NPV for the detection of IFL breaths
by the polynomial model compared with the standard method using
standard formulas (18).
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RESULTS |
Protocol 1
Step 1: curve fitting.
The results of the curve fitting are presented in Table
2. There was a significant difference
between the R2 values when all the breaths are
combined and for the NIFL and IFL breaths when analyzed separately
(P < 0.001 for all three comparisons). For NIFL
breaths, post hoc testing showed that R2 was
significantly larger for the polynomial function compared with all
other functions and that the quadratic function had a larger mean
R2 compared with the other three functions. For
IFL breaths, there was no difference in the mean
R2 values between the quadratic, polynomial, and
double-hyperbolic functions. All three functions had larger mean
R2 values compared with the single-hyperbolic
and exponential functions. For all breaths combined, mean
R2 was highest for the polynomial function; in
addition, R2 values were higher for the
quadratic equation compared with the other three functions. In summary,
the polynomial and quadratic functions had better fits to the data than
the single- and double-term hyperbolic and exponential functions.
Therefore, further analysis was performed only on the quadratic and
polynomial functions.
Step 2: error fit.
Representative graphs depicting the relationship between the actual
pressure-flow curve and the curve as predicted by either the quadratic
or polynomial equations for one IFL and one NIFL breath are illustrated
in Fig. 3. As can be seen, there is more overlap (less error) between
the actual and predicted curves for the polynomial function than for
the quadratic function. For the total group of 50 breaths, the error
fits for the polynomial function were smaller on average than the
quadratic function for the IFL breaths (2.0 ± 2.7 vs. 25.0 ± 22.2%; P < 0.001), NIFL breaths (4.0 ± 7.7 vs. 16.0 ± 14.0%; P = 0.003), and all breaths
combined (3.3 ± 0.06 vs. 21.1 ± 19.0%; P < 0.001).
In summary, in protocol 1, we showed that curve fitting the
pressure-flow relationship in the upper airway will result in a tight
fit (high R2) of the data only for the quadratic
and polynomial functions. However, when a test that determines the
degree of correlation between the actual and experimental relationships
(error fit) was used, only the polynomial function accurately predicts
the pressure-flow relationship.
Protocol 2
Step 1.
The sensitivity, specificity, PPV, and NPV for the detection of flow
limitation in the initial 50 breaths by using the polynomial function
is summarized in Table 3. As the table
illustrates, use of the slope at maximal flow of the polynomial
equation results in both high sensitivity and specificity for
determination of IFL breaths. PPV and NPV were also high. For the
quadratic function, we confirmed that the majority of breaths of both
NIFL (24 of 25; 96%) and IFL (22 of 25; 88%) breaths had a negative
slope, indicating that the quadratic function would be unhelpful in
detecting IFL breaths.
Step 2.
In the larger group of breaths, sensitivity and specificity remained
high (Table 3, right column), as did PPV and NPV.
In summary, in protocol 2, we performed a
sensitivity/specificity analysis of the use of polynomial function to
detect IFL breaths compared with the standard method using a
pressure-flow loop. This analysis indicates that the polynomial
function has an excellent ability to predict the presence of flow
limitation in the pressure-flow relationship. In contrast, the
quadratic function cannot be used to distinguish between IFL and NIFL breaths.
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DISCUSSION |
There are two major findings of this study. First, a polynomial
equation, F(P) = AP3 + BP2 + CP + D,
provides an estimation of the upper airway pressure-flow relationship
with relative precision compared with other mathematical equations.
Second, the derivative of this equation can be used to objectively and
precisely determine the presence of IFL. The main requirement for the
accurate determination of IFL with the use of the polynomial function
is a continuous and simultaneous measurement of flow and supraglottic pressure.
The relationship between flow and pressure in the upper airway during
wakefulness was first described by Rohrer using the equation: P = K1 + K22,
where is flow and K1 and K2 are
constants (16). Hudgel et al. (9) noted that
the pressure-flow relationship during sleep was curvilinear and
therefore less likely to be adequately described by the Rohrer
equation. Instead, they determined that a hyperbolic function (see
Table 1) better characterized the upper airway pressure-flow
relationship during sleep, as indicated by a correlation coefficient of
0.89 compared with 0.55 for the Rohrer equation. They hypothesized that
the characterization was better because the hyperbolic equation
approximated the pressure-flow relationship for both NIFL and IFL
breaths. Similarly, Tamisier and colleagues (20) recently
found that the hyperbolic equation better characterized the
pressure-flow relationship, as evidenced by larger Pearson's square
correlations for all breaths analyzed as well as for the subset of IFL
breaths. In contrast, we found that a three-term polynomial function
best characterized the pressure-flow relationship during sleep. In
addition, we found that a hyperbolic function provided a poor
characterization of the pressure-flow relationship.
There are possible explanations for the different findings. First,
although the Rohrer equation is a polynomial function, it is only a
two-term quadratic function. Our data indicate that a three-term
function provides a better fit of the pressure-flow relationship than a
two-term function. Neither of the previous groups tested a three-term
polynomial function. Second, it should be noted that we performed our
curve fitting on the raw pressure-flow data. Therefore, our pressure
points were negative in value at the time of the curve fitting. The
other groups used pressure values that had been transformed to positive
pressures before curve fitting. The importance of this difference is
illustrated in Fig. 6. As can be seen, if
positive values are used for pressure values, a hyperbolic curve does
closely approximate the actual pressure-flow relationship (Fig.
6B). However, if negative values are used, a hyperbolic
curve does not approximate the relationship (Fig. 6A). We
believe that our use of the negative values for pressure is proper
because the mathematical equations for curve fitting were derived to
determine the relationship between predicted and observed (or actual),
not transformed, variables (14).
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Fig. 6.
A: graphic representation of an IFL breath
(solid line) and the fitted hyperbolic function (dashed line) when flow
is fit to raw pressure data. B: graphic representation
of the same IFL breath (solid line) and the fitted hyperbolic function
(dashed line) when flow is fitted to pressure data transformed to the
absolute value. Note that, in A, a hyperbolic curve provides
a poor representation for the actual pressure-flow relationship,
whereas, in B, a hyperbolic curve provides a reasonable
representation of the pressure-flow relationship.
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Limitation of Methods
The theoretical approach presented at the beginning of the paper
has one major potential limitation. In particular, to apply Newton's
expansion law, we had to create a constant, G, that contains multiple
parameters including density, area, atmospheric pressure, and the
kinematic heat ratio. Therefore, for G to be a constant, these parameters must be assumed to be constant during flow between points M1 and M2. The assumption that density
and the kinematic heat ratio are constants has been made by others
(11) and is based on thermodynamic principles
(19). Area has also been assumed to be a constant by
Rohrer (16). However, it has been shown that
nasopharyngeal area will change during a flow-limited breath (10). In our model, the downstream area
(A2) is the area at the level of the
supraglottic pressure catheter, and we do not know of a study that
shows that area of the supraglottic space changes during inspiration in
normal subjects. In contrast, oropharyngeal and hypopharyngeal area
have been shown to change in patients with sleep apnea
(15). Therefore, we we cannot be certain that G
is a constant during any given breath. Nevertheless, the excellent agreement between the measured data and polynomial function data supports the validity of the assumptions, including that area is a
constant, that were made while developing the theoretical background.
To ascertain the accuracy of mathematical detection of IFL, we had to
use a "benchmark" for detection of flow limitation. We chose an
arbitrary degree of dissociation between pressure and flow for a 1-cm
decrement in supraglottic pressure, based mainly on our ability to
identify such a decrement in pressure. However, the physiological
consequences of such a mild degree of IFL are not known. Conversely,
mathematical methods and visual methods were remarkably reproducible,
indicating that our choice of parameter was valid for the recognition
of the phenomenon. Our study provides an objective operational
definition, which can be used in future studies to ascertain
physiological relevance.
IFL in our study was evaluated as a dichotomous variable. However,
deviation from linearity between flow and pressure is a continuous
variable. Our method detects flow limitation as defined by a plateau in
flow only; any other alinear flow profile is classified as nonflow
limitation. One could argue that changes in the slope of the
pressure-flow relationship indicate pharyngeal narrowing and turbulent
flow. In fact, these were the breaths missed by the mathematical
equation. However, we doubt the physiological significance of deviation
from linearity without true flow limitation.
Finally, detection of IFL in our study required the use of supraglottic
pressure measurement via a pharyngeal catheter and quantitative flow
measurement with the use of a sealed mask and a pneumotachometer. This
combination is rather intrusive and may not be feasible for routine
clinical use. Whether IFL can be detected from the flow vs. time
profile is yet to be determined.
Implications
The ability to detect IFL objectively may have significant
relevance to the diagnosis of SDB. The description of UARS expanded the
spectrum of SDB by including patients without episodes of apnea or
identifiable hypopnea (5). The main features of UARS are
the recurrent arousal due to repetitive episodes of IFL and decreases
in esophageal pressure. Recent studies have shown a moderate
correlation between the number of respiratory events, including periods
of IFL, and daytime sleepiness (7). Unfortunately, detection of IFL was based on subjective visual detection of a square
flow profile without pressure measurements. Conversely, manual analysis
of the pressure-flow loop is laborious and fraught with subjective
pitfalls. We have shown that the polynomial function is both highly
sensitive and specific for the determination of the presence of flow
limitation. Thus our method can be used on a large number of breaths in
an automated fashion and may be useful in future studies that assess
the relationship between SDB and other variables. For instance, we have
recently shown that the percentage of breaths that are IFL is related
to BMI and upper airway resistance (17) and to the
presence of long-term facilitation (3). Therefore, we
hypothesize that a determination of the presence of flow limitation may
provide an alternative metric to assess the relationship between SDB
and daytime consequences, such as excessive daytime sleepiness and
cardiovascular morbidity, particularly in nonapneic forms of the syndrome.
| |
FOOTNOTES |
Address for reprint requests and other correspondence:
J. A. Rowley, Assistant Professor of Medicine, Sleep
Disorders Center at Hutzel Hospital, 4707 St. Antoine, 1 Center,
Detroit, MI 48201 (E-mail:
jrowley{at}intmed.wayne.edu).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
May 31, 2002;10.1152/japplphysiol.01140.2001
Received 16 November 2001; accepted in final form 28 May 2002.
| |
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J APPL PHYSIOL 93(3):1084-1092
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