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1 Department of Medicine, ABSTRACT Hsia, C. C. W., C. J. C. Chuong, and R. L. Johnson, Jr.
Red cell distortion and conceptual basis of diffusing capacity estimates: finite element analysis. J. Appl.
Physiol. 83(4): 1397-1404, 1997.
Roughton-Forster technique; morphometry; pulmonary diffusing
capacity; membrane diffusing capacity; random linear intercept; capillary model
INTRODUCTION USING THE FINITE ELEMENT method (FEM) (1), we
previously showed that diffusive uptake of CO
(DLCO)
across a geometric model of a pulmonary capillary segment is dependent
on the spacing of red blood cells (RBCs), or the hematocrit, within the
capillary (10). If the RBCs are assumed to be circular, the
Roughton-Forster (RF) technique (13) accurately recovers the
conductance of the tissue-plasma membrane (membrane diffusing capacity;
DMCO) at a low hematocrit but modestly overestimates
DMCO as
hematocrit increases; errors arise because conductance of the membrane
for CO varies with alveolar PO2
(PAO2), a feature neglected
in the RF technique. The morphometric technique (19) greatly
overestimates
DMCO,
particularly at a low hematocrit, because the true tissue-plasma
diffusion distance is underestimated and the effective membrane
utilized for diffusion is overestimated.
However, under dynamic flow conditions, RBCs become distorted and
assume a variety of asymmetric shapes, including parachute-like shapes
(15). Such deformation of the RBC reduces shear stress and flow
resistance (2, 3) but can have deleterious effects on diffusive gas
exchange (17). Shape distortions might also exaggerate the conceptual
errors inherent in the RF and morphometric techniques of estimating
DLCO,
although the magnitude of such effects has never been examined. We have
utilized the geometric model and analytic approach described previously
(10) to examine the effect of shape change of RBCs on the diffusive
uptake of CO estimated by different methods.
METHODS
To understand
the effects of dynamic shape distortion of red blood cells (RBCs) as it
develops under high-flow conditions on the standard physiological and
morphometric methods of estimating pulmonary diffusing capacity, we
computed the uptake of CO across a two-dimensional geometric capillary
model containing a variable number of equally spaced RBCs. RBCs are
circular or parachute shaped, with the same perimeter length. Total CO
diffusing capacity (DLCO)
and membrane diffusing capacity
(DMCO)
were calculated by a finite element method.
DLCO
calculated at two levels of alveolar PO2 were used to estimate
DMCO by the
Roughton-Forster (RF) technique. The same capillary model was subjected
to morphometric analysis by the random linear intercept method to
obtain morphometric estimates of
DMCO. Results show that
shape distortion of RBCs significantly reduces capillary diffusive gas
uptake. Shape distortion exaggerates the conceptual errors inherent in
the RF technique (J. Appl. Physiol.
79: 1039-1047, 1995); errors are exaggerated at a high capillary
hematocrit. Shape distortion also introduces additional error in
morphometric estimates of
DMCO caused
by a biased sampling distribution of random linear intercepts; errors are exaggerated at a low capillary hematocrit.
CO) is modeled as a resistance to CO
diffusion across a thin RBC membrane; the resistance is varied in
accordance with the assumed
PAO2 (in Torr) to accurately
mimic the values of CO measured by Holland (9) in dog RBCs at
39°C
Dimensions
and constants employed (6, 9, 12) are listed in Table 1.
(1)
Fig. 1.
Geometric model of a pulmonary capillary segment containing equally
spaced parachute-shaped red blood cells. Dimensions are shown in Table
1. FEM, finite element method.
[View Larger Version of this Image (16K GIF file)]
Table 1.
Dimensions and constants of capillary model
Length of capillary segment
100.0 µm
Alveolar septal
thickness
10.0 µm
Thickness of tissue barrier
1.0 µm
Internal capillary diameter
8.0 µm
RBC diameter
7.5
µm
Thickness of RBC membrane
0.1 µm
Perimeter of RBC on
cross section
23.56 µm
Alveolar PCO
1.0 Torr
DCO*
Air
2.41 × 107 µm2/s
Tissue and
plasma
2.45 × 103 µm2/s
*
2.36 × 10
5 Torr1
CO*, 
80 Torr
2.47
µm3 · s
1 · Torr
1 · RBC1
560 Torr
0.86
µm3 · s
1 · Torr
1 · RBC1
RBC, red blood cell;
CO, specific rate of CO
uptake by RBC and binding with hemoglobin; , Bunsen solubility
coefficient in lung tissue; DCO, diffusion
coefficient for CO.
*
Values measured 39°C.
Assuming 5.1 × 109 RBCs/ml blood.
where
(2)
is Bunsen solubility coefficient in lung tissue,
DCO is diffusion
coefficient, and 
is gradient operator (=
i · 
/x + j · /y + k · /z).
The boundary conditions are PCO = 1 Torr in the alveolar phase 5 µm above the air-tissue interface and PCO = 0 Torr at the inner
membrane surface of the RBCs. Because RBCs are equally spaced and
symmetric with respect to the longitudinal axis of the capillary
segment, we need only examine one typical unit consisting of one-half
of an RBC and its surrounding membrane-plasma barrier and air (Fig. 1).
This unit is divided into 1,264 connecting quadrilateral elements and
1,200 nodal points, each with its own respective diffusion properties in air, tissue, and plasma (Fig. 2). Through this discretization process,
Eq. 2 is transformed into 1,100 simultaneous algebraic equations (excluding boundary constraints), from
which the PCO at each nodal
point can be solved as described previously (10). The matrix equation
has the form
or
Once
the distribution of PCO is
determined, the diffusive flux of CO for each element is computed as
(3)
where
(4)
PCO/n
denotes PCO gradients evaluated
along the normal direction from a constant
PCO surface. The total CO flow, equivalent to
DLCO of
each typical region, is obtained by summing the flow along the boundary
surface of the air-tissue barrier for all the elements
where
PACO is the
mean alveolar PCO at the
air-tissue interface. The
DLCO of the
entire capillary segment is obtained by multiplying
DLCO of a
typical unit by the number of units in the geometric model.
DMCO is
computed by the FEM
[DMCO(FEM)]
as follows
(5)
A
commercial software package (ANSYS, Swanson Analysis System) running on
a DECstation 5000 computer was employed for this analysis. We computed
DLCO using
different numbers of equally spaced RBCs per capillary segment (i.e.,
different capillary hematocrit) and at 80 and 560 Torr
PAO2. Analysis was carried
out for as many RBCs as could be packed into a 100-µm capillary
without overlapping adjacent RBCs, i.e., 13 circular and 17 parachute-shaped RBCs. Parachute-shaped cells can be packed closer
without overlap between cells.
(6)
Fig. 2.
Finite element mesh showing basic unit used in analysis consisting of
one-half of a parachute-shaped red blood cell (RBC) and its surrounding
plasma, tissue, and air. Unit is divided into multiple connecting
triangular and quadrilateral elements.
[View Larger Version of this Image (41K GIF file)]
where
(7)
CO is the specific rate of CO
uptake by RBC and binding with hemoglobin (in ml
CO · ml
blood1 · min1 · Torr1)
and Vc is the total pulmonary
capillary blood volume (in ml). Because
Vc and the number of capillary
RBCs are equivalent quantities as long as RBC volume and capillary
hematocrit are known, we modified Eq. 7 as follows
The
DMCO and
number of RBCs recovered by Eq. 8
[DMCO(RF)]
were compared with the anatomically defined number of RBCs and DMCO
determined by FEM.
(8)
|
(9) |
, derived from stereological principles,
was introduced into Eq. 9 to correct
for the mean intercept angle and to estimate the harmonic mean
thickness of the tissue-plasma barrier
(
hb) in a direction
perpendicular to the epithelial surface (7, 20)
|
(10) |
|
(11) |
hb
in Eq. 11 greatly underestimates true
diffusive resistance of the barrier. Analysis of the flux of CO
suggests that application of the statistical factor is
inappropriate; i.e., the randomly oriented
lhb is a better index of mean path length of molecular diffusion than the
hb oriented perpendicular to
the epithelial surface. Hence, in the present study we also calculated
DMCO(morphometry)
using lhb
|
(12) |
RESULTS
Diffusing capacity estimated by FEM. Figure 4 shows total DMCO for the capillary as well as DMCO per RBC estimated by FEM at two levels of PAO2. This analysis again shows that conductance of the tissue-plasma membrane for CO decreases as PAO2 increases; thus, for a given number of parachute-shaped RBCs in the capillary, estimated DMCO is lower at a higher PAO2. This is because PO2 alters the distribution of local PCO gradients. At a low PAO2, PCO gradients and CO uptake are greater over the RBC surface closest to the endothelium (where mean diffusion path length is short); very little CO uptake occurs across the lateral surface of each RBC. At a high PAO2, PCO gradients and, hence, CO uptake over the surface of each RBC become more uniform (i.e., mean diffusion path shifts to a longer length); hence, resistance of the membrane component increases. DMCO per RBC remains almost constant as the number of RBCs per capillary increases up to about six RBCs per capillary; beyond this point DMCO per RBC progressively declines as the number of RBCs increases. This decline occurs because adjacent cells are sufficiently close that they compete for CO flux across the same intermediate endothelial surface between cells. Hence, above six RBCs per capillary, the increase in total DMCO due to increased number of RBCs is counterbalanced by a fall in DMCO per RBC. Beyond ~15 RBCs per capillary, total DMCO per 100-µm capillary approaches a plateau. A similar pattern is seen for DLCO estimated by FEM (not shown).
For a given number of RBCs in the capillary model, DMCO(FEM) per 100-µm capillary and DMCO(FEM) per RBC are lower for parachute-shaped than for circular RBCs (Fig. 5); the difference diminishes as the number of RBCs increases (17% lower at 1 RBC per capillary and 8% lower at 13 RBCs per capillary). A similar pattern is seen in DLCO estimated by FEM (13% lower at 1 RBC per capillary and 6% lower at 13 RBCs per capillary).
Diffusing capacity estimated by morphometric method. Figure 6 shows the changes in mean linear diffusion path between the epithelial surface and the RBC membrane (lhb); for a given number of capillary RBCs, lhb is significantly longer for parachute-shaped than for circular RBCs. Comparison of DMCO per 100-µm capillary estimated by different methods is shown in Fig. 7 for circular and parachute-shaped RBCs. When the harmonic barrier thickness (
hb) is used to estimate the
path length for diffusion (Eq. 11),
morphometric estimates are grossly elevated compared with corresponding
estimates by FEM for both RBC shapes. Differences between FEM and
morphometric estimates diminish as the number of capillary RBCs
increases. Morphometric estimates range from 352% (2 cells) to 52%
(12 cells) higher than corresponding estimates by FEM for circular RBCs
and from 418% (2 cells) to 57% (16 cells) higher for parachute-shaped
RBCs. As the number of capillary RBCs increases, morphometric
overestimation of
DMCO
diminishes more rapidly for parachute-shaped than for circular cells.
At 10 cells per 100-µm capillary, overestimation of
DMCO is
similar for circular and parachute-shaped cells. Above 10 cells per
100-µm capillary, overestimation of
DMCO is
slightly greater for circular cells. When values at the same number of
RBCs per 100-µm capillary are compared, morphometric estimates of
DMCO are
5% (2 cells) and 16% (12 cells) lower for parachute-shaped than for
circular cells. Similarly, morphometric estimates of
DLCO are
2% (2 cell) to 13% (12 cells) lower for parachute-shaped than for
circular cells.
hb
(Eq. 11) or
lhb
(Eq. 12). RF, Roughton-Forster technique.
Figure 8 shows the ratio of morphometric DMCO estimated using lhb (Eq. 12) to DMCO estimated by FEM. We previously showed that lhb more accurately reflects the molecular diffusion distance than does
hb (10); Eq. 12 yields significantly lower estimates of
DMCO and
DLCO than
Eq. 11, i.e., smaller differences than
estimates by FEM, particularly at low numbers of capillary RBCs. In
fact, above 10 parachute-shaped RBCs per capillary,
DMCO(morphometry) calculated using
lhb is slightly
(5-10%) below corresponding
DMCO estimated by FEM. This slight underestimation disappears at 16 parachute-shaped cells per 100-µm capillary when the cells are almost
maximally packed.
Diffusing capacity estimated by RF method. Deviations of DMCO(RF) from DMCO(FEM) are modest (Fig. 9). At a low hematocrit (<6 RBCs), DMCO(RF) for circular RBCs is 2% higher than corresponding DMCO(FEM), whereas DMCO(RF) for parachute cells is 5% higher than DMCO(FEM). As capillary hematocrit increases, errors in DMCO(RF) increase progressively for both RBC shapes to reach ~9-13% above corresponding DMCO(FEM).
DISCUSSION
The importance of capillary hematocrit in determining capillary resistance to CO diffusion has again been demonstrated, as in our previous analysis using circular RBCs. The present analysis also reveals that shape distortion of RBCs, as it develops under high-flow conditions, significantly reduces diffusive uptake of CO in the lung capillaries. In addition, shape distortion of RBCs exaggerates the overestimation of DMCO caused by conceptual simplifications inherent in the RF technique. Shape distortion also exerts complex effects on the errors inherent in the morphometric technique of estimating DMCO. These effects are modulated by spacing between adjacent RBCs and are discussed below.
Hematocrit and RBC distribution. By the classic concept of diffusive gas transfer in the alveoli, the rate of gas uptake is dependent on the diffusivity of the gas in tissue and plasma, the alveolar-capillary surface area, and the diffusion distance across the alveolar-capillary-plasma barrier. This concept does not formally consider the particulate nature of RBCs. Packaging hemoglobin within discrete RBCs retains the respiratory pigment within the vascular space and avoids the undesirable effects of hemoglobin on vascular tone. On the other hand, it leads to an inherently nonuniform distribution of hemoglobin, i.e., a mismatch of gas exchange surfaces between the RBC and the capillary endothelium. The distribution of RBCs within capillaries is a complex function of interactions among quantity, size, and deformability of RBCs, local flow dynamics, and physical properties of the capillary network. The flow and distribution of RBCs are also affected by margination and sequestration of leukocytes in capillaries (11). That static and dynamic properties of RBCs can alter diffusive gas exchange is shown by various recent reports. Geiser and Betticher (5) reported in isolated perfused rabbit lung that pulmonary diffusing capacity for O2 (DLO2) was lower when the lung was perfused with RBC suspensions than with hemoglobin solutions. Federspiel (4) modeled RBCs as spheres flowing in single file through a cylindrical capillary surrounded by a uniform annulus of alveolar tissue and reported a reduction in membrane diffusing capacity for O2 with increasing RBC spacing (or decreasing hematocrit) greater than the associated reduction in RBC diffusing capacity. Vock and Weibel (16) showed in rabbit lungs that massive hemorrhage led to a significantly reduced DLO2 estimated by morphometric methods. Similar effects of hematocrit on diffusive gas uptake have been reported in skeletal muscles (8). We previously examined the uptake of CO (DLCO) in a single pulmonary segment containing various numbers of circular RBCs and found changes induced by hematocrit similar to those reported by Federspiel for O2. In addition, this kind of analysis allows us to dissect the sources of conceptual errors inherent in the physiological and morphometric methods of estimating diffusing capacity (10). Deformation of RBCs. Effects of RBC deformation on gas transport have been modeled in a single capillary by Wang and Popel (17), who reported that a change from circular to parachute-shaped RBCs decreases O2 flux by 26%; this shape effect is inversely related to the RBC residence time within the capillary. Betticher et al. (2) demonstrated in isolated rabbit lungs that reduced RBC deformability reduces DLO2. They attribute this effect to the resistance offered by a thicker unstirred layer of plasma outside the RBC membrane; thickness of the unstirred layer is enhanced around undeformed RBCs flowing at low velocities and diminished by the increased mixing associated with deformation of RBCs at high flow velocities. Sarelius (14) points out an alternative explanation for the observation of Betticher et al.; i.e., reduced deformability of RBCs is associated with less uniformity of resistance to RBC flow in the capillaries, leading to nonuniform regional hematocrits. Our present analysis is consistent with the finding of Wang and Popel (17) that the shape distortion of the RBC that occurs under high-flow conditions can significantly impair the DLCO across the capillary. This theoretical impairment is due to a greater inhomogeneity in the distribution of CO flux over the surface of each RBC, but such a deleterious effect may be offset by simultaneous improvements in hydrodynamics of the deformed cells, which might lead to greater homogeneity in the distribution of capillary hematocrits. Errors in physiological estimate of diffusing capacity. Our previous analysis shows that, within the geometric capillary model containing circular RBCs, DMCO(RF) estimates are modestly higher than DMCO(FEM) estimates at hematocrits at or above physiological level. This overestimation occurs because the RF technique assumes DMCO to be constant regardless of PAO2. Finite element analysis has shown that, in fact, DMCO estimated as CO flux decreases as PAO2 increases, because distribution of PCO over the RBC surface becomes more uniform, and as a consequence the distribution of molecular diffusion paths shifts toward longer lengths. Reducing PAO2 (i.e., increasingCO in Eq. 7) increases CO flux into the RBC, and at the higher
rates of flux CO uptake by RBCs preferentially shifts to areas of the
RBC surface nearer the alveolar-capillary surface, thereby reducing
mean diffusion distance. The resulting error in the RF technique,
caused by assuming a constant
DMCO as
CO changes, is further
exaggerated by shape distortion of RBCs, because for a given number of
capillary RBCs, the effect of
PAO2 on flux distribution is
greater for parachute-shaped than for circular RBCs (Fig. 3) (10). The
magnitude of overestimation for parachute-shaped cells increases to
13% at the highest number of RBCs that can be packed into a capillary
segment without overlap.
Errors in morphometric estimate of diffusing capacity.
On the other hand, previous analysis shows that estimates of
DMCO by
Weibel's morphometric technique are grossly elevated with respect to
estimates by FEM when the number of capillary RBCs is low, but
differences progressively diminish as the number of capillary RBCs
increases. Much of the discrepancy between morphometric and FEM
estimates could be attributed to an error in the stereological construct, which imposes an arbitrary factor of to correct
for the angle between the mean random linear intercept from the
epithelium to the RBC membrane and the normal to the epithelial
surface. When this arbitrary factor was omitted, agreement between
these two methods becomes much closer in the physiological range of
hematocrits (10). Overestimation of
DMCO by
morphometry is moderately exaggerated by shape distortion of the RBCs
when the number of capillary RBCs per 100-µm capillary is <10 (Fig. 8). At >10 RBCs per 100-µm capillary, morphometry (using
lhb rather than
hb to estimate mean barrier
distance) actually underestimates true
DMCO by up
to 10%. This seemingly paradoxical pattern can be explained by several
observations that lead to opposing effects that counterbalance one
another as the number of capillary RBCs increases.
1) The morphometric technique
measures the distance of randomly oriented linear diffusion paths from
the epithelial surface to the RBC surface, whereas FEM reveals that
local PCO gradients constrain CO
flux by diffusion to markedly curvilinear paths over much of the RBC
surface. This curvilinearity is more pronounced for parachute-shaped
than for circular RBCs and also more marked when RBCs are far apart
than when they are close together. Thus approximation of diffusion
distance using random linear intercepts as employed in the morphometric
method yields an underestimation of true diffusion distance and an
overestimation of
DMCO. As
more RBCs are packed into the capillary, the mean diffusion path
becomes shorter and more nearly linear; thus errors in
DMCO due to
measured values of mean linear path length
(lhb)
progressively diminish. 2) The
morphometric method utilizes the entire available alveolar-capillary surface area in the calculation of
DMCO
regardless of the number of capillary RBCs. However, FEM analysis
demonstrates that most of the CO flux occurs across only a small
portion of the tissue membrane close to an RBC. As the number of
capillary RBCs increases, the distribution of CO flux along the
alveolar-capillary surface becomes more uniform; i.e., the effective
alveolar-capillary surface available for diffusive gas exchange
increases and approaches that estimated by morphometry. Thus
morphometry grossly overestimates DMCO at a
low hematocrit, and errors diminish progressively as capillary
hematocrit increases. 3) The error
in morphometry caused by underestimation of molecular diffusion
distance due to linear approximation of a curvilinear diffusion path is
counterbalanced in parachute-shaped cells by another error arising from
a biased sampling distribution over the RBC surface. This source of
error is related to RBC geometry and the probability that some portions of the infolded perimeter of the parachute-shaped cell are
preferentially sampled by a randomly oriented line, particularly as RBC
spacing diminishes (Fig. 10). The
probability of sampling any given point along the infolded perimeter of
a parachute-shaped RBC by a randomly oriented line through a given
point on the epithelial surface (point
a) varies from a finite value
(regions 1 and
3) to zero (region
2), even though these regions subtend the same angle. Because of the concentration gradient of CO and the axial symmetry of
the capillary segment, according to FEM most of the CO flux across
point a will reach
region 3 of the RBC, whereas a random linear intercept from point a to
region 1 in fact violates physical laws by running against the local
PCO gradient. Therefore, by the
random linear intercept method, a significant portion of the infolded
RBC perimeter closest to point a is
undersampled, whereas the regions farthest from
point a are oversampled. The net
result of this sampling bias is an overestimation of mean diffusion
path length over the infolded surface of the RBC, leading to an
underestimation of
DMCO. As
the number of capillary RBCs increases, this sampling bias increases.
However, beyond a certain closeness of RBC packing (16 cells per
capillary), this bias disappears, because lateral surfaces of adjacent
RBCs become relatively hidden and inaccessible to linear sampling from
the epithelial surface. Hence, the apparent mean barrier thickness
again decreases (Fig. 6) and morphometric DMCO
abruptly increases (Fig. 7). This sampling bias arises for parachute-shaped but not circular RBCs, because parachute-shaped cells
lack full rotational symmetry. We would expect a similar sampling bias
to occur in other asymmetric shapes assumed by RBCs.
Limitations of FEM. As pointed out previously (10), our model is not meant to reproduce reality but, rather, to provide a uniform framework and an independent analytic technique that could be utilized to explore the conceptual basis of our understanding of the pulmonary diffusion process and to reconcile differences between current physiological and morphometric methods of estimating pulmonary diffusing capacity. This stylized capillary model is two-dimensional and static; no motion of RBCs is implied. The selection of cell shapes is necessarily arbitrary, since RBCs, in fact, can assume numerous irregular shapes during capillary transit. However, the circular and parachute shapes are representative of a symmetric and an asymmetric configuration, respectively. Furthermore, the parachute is a shape seen in perfused capillaries under direct observation. The boundary conditions are also arbitrary, but variations would not have altered our general conclusions. The primary variable examined in this study is DMCO and the potential sources of error in its estimation by the RF and the morphometric methods; we assumed that in vitro measurements of
CO at different levels of
PO2 are correct. For the sake of
simplicity, the reaction kinetics of
O2 displacement by CO are not
explicitly included in the model. We have employed the same values of
CO for the FEM, morphometric, and RF estimations of
DMCO; the
conclusions drawn are independent of the accuracy of the relationship
between 1/CO and
PO2 and of the reaction kinetics
inside the RBCs.
We conclude from finite element analysis that shape distortion of the
RBCs as develops under high-flow conditions alters the distribution of
CO flux across the RBC surface and reduces the diffusive uptake of CO.
Distortion of RBCs exaggerates conceptual errors in the RF and the
morphometric technique of estimating diffusing capacity via different
mechanisms. Errors in the RF technique arise from the same source
regardless of RBC shape and are most sensitive to changes in RBC
spacing in the physiological range of hematocrits. The various sources
of error in the morphometric technique exert opposing effects on the
estimate of
DMCO; their net effect is most sensitive to changes in RBC spacing when the capillary hematocrit is low. In vivo, the unfavorable effect of RBC
shape distortion on diffusive gas uptake may be mitigated by its
favorable effect on hydrodynamics and the distribution of capillary RBC
flow.
ACKNOWLEDGEMENTS
This project was supported by National Heart, Lung, and Blood Institute Grants R01-HL-40070, R01-HL-45716, and RO1-HL-46185. C. C. W. Hsia was supported by an Established Investigator Award from the American Heart Association.
FOOTNOTES
Address for reprint requests: C. C. W. Hsia, Dept. of Medicine, University of Texas Southwestern Medical Center, 5323 Harry Hines Blvd., Dallas, TX 75235-9034.
Received 31 January 1997; accepted in final form 2 June 1997.
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S. C. Kanick, W. J. Doyle, S. N. Ghadiali, and W. J. Federspiel On morphometric measurement of oxygen diffusing capacity in middle ear gas exchange J Appl Physiol, January 1, 2005; 98(1): 114 - 119. [Abstract] [Full Text] [PDF]
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L. K. Nabors, W. A. Baumgartner Jr., S. J. Janke, J. R. Rose, W. W. Wagner Jr., and R. L. Capen Red blood cell orientation in pulmonary capillaries and its effect on gas diffusion J Appl Physiol, April 1, 2003; 94(4): 1634 - 1640. [Abstract] [Full Text] [PDF]
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C. C. W. Hsia, R. L. Johnson Jr., and D. Shah Red cell distribution and the recruitment of pulmonary diffusing capacity J Appl Physiol, May 1, 1999; 86(5): 1460 - 1467. [Abstract] [Full Text] [PDF]
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