Download Oxygen delivery to skeletal muscle fibers

Am J Physiol Heart Circ Physiol 285: H955–H963, 2003.
First published May 8, 2003; 10.1152/ajpheart.00278.2003.
Oxygen delivery to skeletal muscle fibers: effects of
microvascular unit structure and control mechanisms
Arthur Lo,1 Andrew J. Fuglevand,2 and Timothy W. Secomb1,2
1
Program in Applied Mathematics, University of Arizona, Tucson 85721; and
Department of Physiology, University of Arizona, Tucson, Arizona 85724
2
Submitted 26 January 2003; accepted in final form 25 April 2003
capillaries; conducted response; flow regulation; motor units;
oxygen diffusion; theoretical model
THE OXYGEN DEMAND of skeletal muscle varies over a
wide range according to its level of activity. To meet
this changing demand, blood flow to muscle also varies
widely. For example, oxygen consumption has been
observed to increase ⬃50-fold, with a 25-fold increase
in blood flow between states of rest and maximal exercise in the knee extensor muscles (4). As the activity
level of a skeletal muscle is increased, additional muscle fibers are recruited in groups (motor units), which
Address for reprint requests and other correspondence: T. W.
Secomb, Dept. of Physiology, Univ. of Arizona, Tucson, AZ 857245051 (E-mail: [email protected]).
http://www.ajpheart.org
are activated in a predetermined sequence until the
desired force of contraction is achieved (9, 18). Each
motor unit consists of a single motor neuron that innervates 20–2,000 fibers distributed throughout the
muscle (5, 6). A mammalian muscle typically contains
50–300 motor units. Oxygen consumption in inactive
motor units remains near the resting level. Therefore,
oxygen demand in a partially activated muscle is
highly nonuniform, with fibers belonging to active motor units interspersed with quiescent fibers.
Oxygen is delivered to skeletal muscle fibers by convective transport in blood flowing in capillaries that
run approximately parallel to the fibers and by diffusion from the capillaries to surrounding muscle fibers.
The availability of oxygen to a given muscle fiber is
therefore dependent on the number of nearby capillaries that are perfused and the rate of blood flow in those
capillaries. Krogh (24) proposed that blood flow is controlled at the level of individual capillaries, such that
the number of flowing capillaries varies in response to
local oxygen demand. According to this concept, flow in
each capillary is regulated by active contraction of the
capillary or of a precapillary sphincter located at the
entrance to the capillary. With regard to skeletal muscle, however, most evidence suggests that capillary
perfusion is regulated primarily by the arterioles. The
group of capillaries fed by a single terminal arteriole is
then the smallest functional unit for control of blood
flow (21). Such a microvascular unit (MVU) typically
contains 20–25 capillaries and supplies a region of
muscle tissue ⬃100 ⫻ 200 ␮m in cross section and with
length 500 ␮m along the fibers (8, 25), as shown in Fig.
1. The region perfused by one MVU necessarily encompasses portions of several adjacent muscle fibers.
A spatial mismatch is evident between the functional
units of muscle activation and of flow regulation. Each
motor unit consists of many dispersed muscle fibers,
each of which is supplied by a number of different
MVUs along its length (12). Conversely, each MVU
supplies several adjacent muscle fibers, which typically
belong to different motor units (33). Given this spatial
mismatch, how is capillary blood flow regulated to
meet local oxygen requirements? More specifically,
how many capillaries must be perfused to ensure adeThe costs of publication of this article were defrayed in part by the
payment of page charges. The article must therefore be hereby
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0363-6135/03 $5.00 Copyright © 2003 the American Physiological Society
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Lo, Arthur, Andrew J. Fuglevand, and Timothy W.
Secomb. Oxygen delivery to skeletal muscle fibers: effects of
microvascular unit structure and control mechanisms. Am J
Physiol Heart Circ Physiol 285: H955–H963, 2003. First
published May 8, 2003; 10.1152/ajpheart.00278.2003.—The
number of perfused capillaries in skeletal muscle varies with
muscle activation. With increasing activation, muscle fibers
are recruited as motor units consisting of widely dispersed
fibers, whereas capillaries are recruited as groups called
microvascular units (MVUs) that supply several adjacent
fibers. In this study, a theoretical model was used to examine
the consequences of this spatial mismatch between the functional units of muscle activation and capillary perfusion.
Diffusive oxygen transport was simulated in cross sections of
skeletal muscle, including several MVUs and fibers from
several motor units. Four alternative hypothetical mechanisms controlling capillary perfusion were considered. First,
all capillaries adjacent to active fibers are perfused. Second,
all MVUs containing capillaries adjacent to active fibers are
perfused. Third, each MVU is perfused whenever oxygen
levels at its feed arteriole fall below a threshold value.
Fourth, each MVU is perfused whenever the average oxygen
level at its capillaries falls below a threshold value. For each
mechanism, the dependence of the fraction of perfused capillaries on the level of muscle activation was predicted. Comparison of the results led to the following conclusions. Control
of perfusion by MVUs increases the fraction of perfused
capillaries relative to control by individual capillaries. Control by arteriolar oxygen sensing leads to poor control of
tissue oxygenation at high levels of muscle activation. Control of MVU perfusion by capillary oxygen sensing permits
adequate tissue oxygenation over the full range of activation
without resulting in perfusion of all MVUs containing capillaries adjacent to active fibers.
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OXYGEN DELIVERY TO SKELETAL MUSCLE FIBERS
Fig. 1. Schematic representation of the geometrical relationship
between a single microvascular unit (MVUs; vessels indicated by
solid lines or dots) and a muscle fiber (shaded area). A, arteriole; V,
venule. Inset: S denotes the location of the cross section.
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METHODS
Configurations of muscle fibers and capillaries. Two photomicrographs of skeletal muscle cross sections were used to
obtain the positions of muscle fibers and capillaries for the
following simulations: 1) a light micrograph from a cryostat
section of rat plantaris stained with a 1% aqueous solution of
toluidine blue (22); and 2) a confocal micrograph from a
cryostat section of rat extensor digitorum longus (EDL) muscles exposed to fluorescein isothiocyanate-conjugated Griffonia simplicifolia I lectin to label capillaries (17) (HansenSmith F., unpublished observations). The two micrographs
were scanned and digitized and then subdivided into pixels
corresponding to 2 ⫻ 2 ␮m regions of tissue. Each pixel was
designated as containing capillary, muscle fiber, or interstitial space as appropriate. A tissue domain with dimensions
600 ⫻ 600 ␮m was used in the simulations. Because the
regions in the photomicrographs were smaller than this, they
were duplicated in a repeating arrangement to fill the domain. For comparison purposes, a third configuration was
considered, consisting of a regular array of identical regular
hexagonal fibers, with three capillaries distributed around
each fiber. The diameter of the fibers in this configuration
was within the range of diameters observed in the literature.
The resulting configurations are shown in Fig. 2. Table 1
summarizes their properties.
Geometry of motor units and MVUs. The grouping of capillaries into MVUs and muscle fibers into motor units could
not be determined from the photomicrographs. Appropriately
sized MVUs were therefore generated by dividing the muscle
cross section into 18 domains 100 ⫻ 200 ␮m in size, with
every capillary inside a given domain grouped into the same
MVU (Fig. 3). The MVUs contained 11–22 capillaries depending on the capillary density of the tissue. The muscle
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quate oxygen supply to active muscle fibers at a given
level of muscle activation?
Fuglevand and Segal (13) addressed these questions
using a theoretical modeling approach. They considered a region in the cross section of a skeletal muscle
that contained a number of motor units and MVUs.
Individual fibers dispersed throughout the muscle
were grouped into physiologically representative motor
units. Each MVU was assumed to supply a region 1 ⫻
1 mm or 0.5 ⫻ 0.5 mm in cross section (3). Perfusion of
a MVU was assumed to occur whenever any muscle
fiber lying within its region was activated. With these
assumptions, the model predicted a highly nonlinear
relationship between the fraction of active fibers and
the fraction of perfused MVUs, with nearly all MVUs
perfused when a small fraction of the muscle fibers was
activated. If, instead, the functional units for blood flow
control coincided with those of muscle activation (3), a
linear relationship would be expected. These results
therefore demonstrated that perfusion of skeletal muscle depends critically on the precise spatial relationship between MVUs and motor units.
This model (13) has evident limitations. First, the
assumed size of the MVUs in the muscle cross section
(1 ⫻ 1 mm or 0.5 ⫻ 0.5 mm) was larger than the size
suggested by observations (0.1 ⫻ 0.2 mm) (25). Second,
all capillaries in a MVU were assumed to flow whenever any fiber in the region was activated. Both assumptions could lead to overestimation of the number
of capillaries that must be perfused when a given
fraction of fibers has been recruited. In reality, MVU
perfusion probably depends on levels of oxygen, potassium, and other metabolites released during muscle
activity, and activation of a single fiber does not necessarily stimulate perfusion of all adjacent capillaries.
Furthermore, the diffusive spread of oxygen through
muscle tissue allows the possibility that an active muscle fiber may receive adequate oxygen supply from
capillaries belonging to nonadjacent MVUs.
On the basis of these considerations, the objective of
the present study was to develop a more realistic theoretical model to examine the relationship between
muscle fiber activation and capillary perfusion in skeletal muscle. The model includes a two-dimensional
simulation of diffusive oxygen transport from capillaries to fibers in a muscle cross section to predict levels of
tissue oxygenation. The mechanisms by which activation of muscle fibers leads to capillary perfusion are not
well established. In the model, the effects of four hypothetical mechanisms were explored. In the first two
mechanisms, capillaries adjacent to active fibers are
activated, independent of oxygen levels, as in the
model of Fuglevand and Segal (13). To show explicitly
the effects of capillary grouping into MVUs, the following two cases were considered: in case A, any individual
capillary adjacent to an active fiber is perfused (“adjacent capillary mechanism”); in case B, any MVU containing one or more capillaries adjacent to an active
fiber is perfused (“adjacent MVU mechanism”). In the
other mechanisms considered, perfusion of MVUs was
assumed to depend on tissue oxygen levels. Two alternative hypotheses regarding this response were considered: in case C, flow is initiated in a MVU whenever
the partial PO2 adjacent to the arteriole feeding that
MVU drops below a threshold value (“arteriolar response mechanism”). This hypothesis assumes direct
arteriolar responsiveness to local PO2 levels (10, 20,
36). In case D, flow is initiated whenever the average
level of PO2 in the tissue adjacent to capillaries of the
MVU drops below a threshold value (“conducted response mechanism”). This hypothesis assumes the existence of mechanisms for transferring information
about tissue oxygenation levels at the capillary level
upstream to the feeding arteriole (19, 38), possibly via
conducted electrical responses (32, 34). For each mechanism considered, the model was used to predict the
number of perfused capillaries and oxygen levels in
tissue as a function of the fraction of active muscle
fibers.
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fibers lying within the tissue region were randomly assigned
to 10 equal groups, each group being dispersed through the
region. To show the effects of increasing levels of muscle
activation, these groups were sequentially activated and the
corresponding changes in oxygen levels and MVU activation
simulated, as described below. This assumption does not
correspond directly to the sequential activation of realistic
motor units, where units with few fibers are typically activated earlier and units with many fibers later (27). However,
introducing heterogeneous motor unit sizes in the present
model would not alter the results for any given fraction of
active fibers, as long as fibers belonging to each motor unit
are randomly dispersed through the tissue region.
Oxygen transport and consumption. Under any given set of
conditions, each capillary was designated as perfused or
unperfused. In perfused capillaries, the PO2 was set at a fixed
level of 45 mmHg, representative of capillary PO2 levels in
active skeletal muscle. Because oxygen transport in a single
muscle cross section is considered, it is not possible to include
explicitly the decline of PO2 along capillaries within the
context of this model. The diffusion of oxygen through tissue
was considered to be unaffected by the presence of unperfused capillaries. Similarly, each muscle fiber was designated
as active or inactive. The basal oxygen demand of inactive
fibers was assumed to be Minactive ⫽ 1 cm3O2 (100 cm3 䡠
min)⫺1 (11). The oxygen demand of active muscle fibers was
assumed to be Mactive ⫽ 16 cm3O2 (100 cm3 䡠 min)⫺1, close to
the maximal rate of working of trained rat hindlimb muscle
(30). The relationship between the oxygen consumption and
tissue PO2 was described by Michaelis-Menten kinetics with
half-maximal consumption at a tissue PO2 of P0 ⫽ 1 mmHg
(7, 29). To assess the overall level of tissue oxygenation, the
“oxygen deficit” was defined as the difference between the
total oxygen demand of the region and the total consumption
computed according to the Michaelis-Menten relationship
divided by the total demand. Consumption falls significantly
below demand only in regions of low PO2, so the oxygen deficit
is a functional index of the amount of hypoxic tissue.
Computation of tissue PO2. A two-dimensional time-dependent diffusion equation was used to compute the distribution
of tissue PO2 within the simulated muscle cross section
⳵P/⳵t ⫽ D␣(⳵2P/⳵x2 ⫹ ⳵2P/⳵y2) ⫺ M0P/(P ⫹ P0)
(1)
where P(x,y,t) represents the PO2 at a point (x, y) at time t and
the symbol ⳵ denotes a partial derivative. The quantity D␣ was
assumed to be a constant, where D is the diffusion coefficient of
oxygen in tissue (1.5 ⫻ 10⫺5 cm2 䡠s⫺1) (1), and ␣ is the solubility
(4 ⫻ 10⫺5 cm3O2 䡠cm⫺3 䡠mmHg⫺1). Within each muscle fiber,
the oxygen demand M0 was set to Minactive or Mactive as appropriate. To minimize the effect of boundary artifacts, periodic
boundary conditions were imposed at the edges of the domain,
i.e., levels of PO2 at each edge of the domain were assumed to
match those at the corresponding point on the opposite edge.
A finite-difference method was used to solve Eq. 1. A 300 ⫻
300 grid was used, corresponding to a spacing of 2 ␮m
between grid points, with a 0.5-ms time step. PO2 values at
all grid points lying within perfused capillaries were set to 45
mmHg. The governing equations were discretized using central differences and solved using an explicit scheme. The
computations were continued until the absolute difference in
tissue PO2 between successive time steps was ⬍2 ⫻ 10⫺4
mmHg at each grid point. The tissue PO2 was assumed to be
at a steady state when this condition was met. In the initial
state, all fibers are assumed to be inactive. It was assumed
that a single, randomly chosen MVU was perfused to meet
the quiescent oxygen demand in this case. The number of
active fibers was then increased as already described, and the
perfused capillaries were determined according to the criteria described below. The steady-state solution was found for
each combination of active fibers and perfused capillaries.
Activation sequence of motor units and MVUs. For each of
the three configurations considered (Fig. 2), increasing acti-
Table 1. Characteristics of muscle cross sections used for simulations
Case
Animal
Muscle
Size of
Region, ␮m
Capillary
Density, mm⫺2
Capillary-toFiber Ratio
A
B
C
Rat
Rat
Plantaris
EDL
Idealized
300 ⫻ 300
400 ⫻ 600
600 ⫻ 600
911
728
897
1.52
1.46
0.92
Source
Kano et al. (22)
Hansen-Smith, unpublished observations
EDL, extensor digitorum longnus.
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Fig. 2. Configurations of muscle fibers and capillaries in 600 ⫻ 600 ␮m skeletal muscle cross sections used in
simulations. Small dots indicate locations of capillaries. Dashed lines show boundaries of original photomicrographs. A: rat plantaris (22); B: rat extensor digitorum longus (EDL) (Hansen-Smith F., unpublished photomicrograph); C: idealized hexagonal array.
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OXYGEN DELIVERY TO SKELETAL MUSCLE FIBERS
vation of the muscle was simulated by sequential recruitment of spatially dispersed groups of muscle fibers. Starting
with the case in which all fibers are inactive, simulations
were carried out for cases where the active fraction of the
total muscle cross section area increased in steps of ⬃0.1.
With each successive increase in the number of active fibers, the
new steady-state distribution of PO2 in the tissue cross section
was calculated according to the procedure described above with
RESULTS
Spatial distributions of active fibers, perfused capillaries, and PO2. Figure 5 shows examples of results
obtained for the rat EDL muscle with the use of the
conducted response mechanism, for two levels of mus-
Fig. 4. Schematic representation of the four alternate
mechanisms considered in the model, by which capillaries are perfused in response to muscle fiber activation. In each case, dark shading indicates an active
muscle fiber. Light shading denotes the resulting low
tissue PO2 region. Dots indicate perfused capillaries,
according to each mechanism. A: adjacent capillary
mechanism. B: adjacent MVU mechanism. C: arteriolar
response mechanism. Dashed trace denotes arteriolefeeding MVU. D: conducted response mechanism.
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Fig. 3. Capillaries are grouped into 1 of 18 MVUs by their location in
the muscle cross section. The dots indicate the location of all capillaries in the rat EDL configuration. All capillaries located within each
box are grouped into a single MVU perfused by the same arteriole. The
diagonal line represents the location of the arteriole perfusing the MVU
denoted by the shaded box.
additional MVUs or individual capillaries perfused as necessary to maintain tissue oxygenation using the chosen mechanism of blood flow regulation. In each case, the variation of the
fraction of perfused capillaries with the fraction of active fiber
area was determined and presented in graphical form.
The four mechanisms of capillary perfusion considered
were implemented in the model as follows (Fig. 4).
Case A: adjacent capillary mechanism. Any capillary lying
adjacent to an active muscle fiber was assumed to be perfused, independent of PO2 levels. This mechanism makes no
reference to MVUs.
Case B: adjacent MVU mechanism. Any MVU containing a
capillary lying adjacent to an active fiber was assumed to be
perfused, independent of PO2 levels.
Case C: arteriolar response mechanism. For each MVU, the
feeding arteriole was represented by a straight segment 200
␮m in length, lying 75 ␮m outside the region supplied by the
MVU (Fig. 3). The minimum tissue PO2 along the segment
was estimated, and the arteriole was assumed to dilate and
perfuse the MVU if the minimum PO2 fell below a specified
critical level.
Case D: conducted response mechanism. For each MVU,
the tissue PO2 at the location of all capillaries in the MVU
was computed. The corresponding arteriole was assumed to
dilate as a result of conducted responses, perfusing the capillaries of the MVU, if the average PO2 at the capillaries fell
below a specified level. A range of critical PO2 values was
considered for the arteriolar response mechanism and the
conducted response mechanism.
OXYGEN DELIVERY TO SKELETAL MUSCLE FIBERS
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cle activation. The expected spatial mismatch between
the locations of active muscle fibers and the domains of
perfused MVUs is evident from a comparison of Fig. 5,
A and B. Figure 5C shows the predicted steady-state
PO2 distributions. Several areas of low PO2 occur when
clusters of active muscle fibers have few perfused capillaries nearby. Conversely, high levels of tissue PO2
occur in regions with no active muscle fibers in close
proximity to a group of perfused capillaries.
A comparison of Fig. 5, left and right, shows the
predicted effect of increasing the fraction of active
muscle fibers from 0.2 to 0.42. In this instance, two
additional MVUs were perfused according to the criteria of the conducted response mechanism, and the
fraction of perfused capillaries increased from 0.42 to
0.54. This increase in oxygen supply was not enough to
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completely balance the increase in demand, and the
oxygen deficit increased from 0.06 to 0.09.
Effects of capillary grouping into MVUs. Figure 6
shows the fraction of perfused capillaries as a function
of active fiber fraction for the adjacent capillary and
adjacent MVU mechanisms. For a given active fiber
fraction, perfusion control by MVUs leads to more
perfused capillaries than individual capillary perfusion
because whenever any capillary is perfused, all other
capillaries in the same MVU are necessarily also perfused. The oxygen deficit is low in all cases and does not
differ appreciably between the two assumed mechanisms. These results show that the grouping of capillaries into functional units triggers the perfusion of
additional capillaries not required to maintain adequate tissue oxygenation.
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Fig. 5. Example of results obtained from
simulations of rat EDL muscle assuming
the conducted response mechanism, for
two different levels of muscle activation.
In each case, results for a 600 ⫻ 600 ␮m
region in the muscle cross section are
shown. A: active fibers (blue) and inactive
fibers (yellow). B: locations of perfused
capillaries. C: distribution of tissue PO2,
color-coded according to the bar (inset).
Left, fraction of active fibers ⫽ 0.2, fraction
of perfused capillaries ⫽ 0.42, and oxygen
deficit ⫽ 0.06. Right, fraction of active fibers ⫽ 0.44, fraction of perfused capillaries ⫽ 0.54, and oxygen deficit ⫽ 0.09.
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OXYGEN DELIVERY TO SKELETAL MUSCLE FIBERS
Effects of mechanisms controlling capillary perfusion. The predicted fractions of perfused capillaries as
a function of active fiber fraction are shown in Fig. 7 for
the arteriolar response mechanism and the conducted
response mechanism. Relative to the adjacent MVU
mechanism (Fig. 6), both the arteriolar response and
the conducted response mechanisms result in substantially lower fractions of perfused capillaries for a given
level of muscle activation, together with higher levels
of oxygen deficit. In the case of the conducted response
mechanism, the oxygen deficit varied with muscle fiber
activation but was not ⬎0.11. In contrast, the oxygen
deficit was not well controlled when the arteriolar
response mechanism was assumed, but generally increased with increasing activation, despite the fact
that the fraction of perfused capillaries was comparable in both cases.
The results shown in Fig. 7 assume a minimum
critical PO2 value of 5 mmHg for the arteriolar response
mechanism and an average critical PO2 value of 7
mmHg for the conducted response mechanism. These
levels were chosen to give comparable levels of capillary perfusion and oxygen deficit at low levels of activation. Further simulations were also carried out in
which the assumed critical PO2 values were varied to
examine the dependence of the results on the chosen
values. For the arteriolar response mechanism, increasing the critical PO2 value did not result in better
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control of tissue oxygenation at high levels of muscle
activation. Not all capillaries were perfused when all
muscle fibers were activated, even when the critical
PO2 value was increased to 11 mmHg. These results
suggest that control of perfusion by arteriolar response
to oxygen levels in adjacent tissue is relatively ineffective in matching oxygen demand and supply. The ability of the conducted response mechanism to control
oxygen deficit over the full range of activation levels
was maintained when the critical PO2 value was varied
between 1 and 13 mmHg.
Effects of fiber and capillary geometry. Similar results were obtained for all three configurations considered (Figs. 6 and 7). The results for the idealized
hexagonal structure did not differ in a systematic way
from the results for configurations derived from photomicrographs. Thus the heterogeneity in fiber size and
capillary spacing observed in vivo does not appear to
have a large impact on the fraction of perfused capillaries needed to supply oxygen under given conditions.
DISCUSSION
In a partially activated skeletal muscle, fibers belonging to active motor units are interspersed with
inactive fibers, and oxygen demand is therefore highly
nonuniform. Similarly, groups of capillaries belonging
to perfused MVUs are interspersed with nonperfused
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Fig. 6. A: fraction of capillaries perfused as a function of fraction of muscle fiber area activated, for the three
configurations used in simulations (left, rat plantaris; middle, rat EDL; right, idealized hexagonal array). B:
corresponding values of oxygen deficit. F, Adjacent capillary mechanism; E, adjacent MVU mechanism.
OXYGEN DELIVERY TO SKELETAL MUSCLE FIBERS
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capillaries, leading to nonuniform tissue perfusion. As
a result of the spatial mismatch between the domains
of motor units and MVUs, some regions of tissue with
high oxygen demand are likely to be underperfused,
whereas other regions with low demand are perfused.
Our simulations (Fig. 5) show that these conditions can
lead to substantial heterogeneity in PO2 levels within
the muscle cross section. Significant changes in tissue
PO2 occurred over a length scale of order from 50 to 100
␮m. In maximally active skeletal muscle, where all
capillaries are perfused and fibers are active, PO2 levels
are also heterogeneous, with steep gradients around
each capillary. However, the scale of the gradients is
then shorter, ⬃20 ␮m (26).
As expected, the grouping of capillaries into MVUs
increases the number of capillaries that must be perfused at a given level of activation, relative to the case
in which perfusion of each capillary is assumed to be
individually controlled (Fig. 6). The results for the
adjacent MVU mechanism are qualitatively similar to
those obtained by Fuglevand and Segal (13), but the
initial rate of increase in capillary perfusion as a function of muscle activation was less steep in the present
study. The lower slope reflects the smaller domain size
of each MVU assumed here, i.e., 100 ⫻ 200 ␮m, compared with 1 ⫻ 1 mm in the Fuglevand and Segal
study, and the inclusion of effects of oxygen diffusion
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when determining which MVUs are perfused in response to increasing fiber activation.
The results shown in Figs. 6 and 7 demonstrate how
inclusion of PO2 as an explicit control signal influences
perfusion within the muscle cross section. Compared
with the simulations in which adjacent active fibers
induced perfusion of MVUs, the simulations in which
oxygen levels were sensed led to a lower fraction of
perfused capillaries, particularly at low levels of muscle activation, while keeping the oxygen deficit relatively low (Fig. 7). Moreover, because oxygen can diffuse to active fibers that are near but not adjacent to
the perfused capillary, this partially compensates for
the geometric mismatch between the functional units.
Low oxygen levels occur only when active fibers are a
distance of ⬃50 ␮m or more from the nearest perfused
capillary. The diffusion of oxygen from regions of
higher concentration to regions of lower concentration
helps to minimize the effects of the irregular shapes of
the muscle fibers and randomly distributed capillary
locations in the observed muscle cross sections, giving
results that were similar to those for an idealized
hexagonal arrangement with approximately the same
capillary density and fiber size.
Results obtained using this model depend on the
assumptions made with regard to the mechanisms
controlling perfusion of capillaries or MVUs. Several
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Fig. 7. A: fraction of capillaries perfused as a function of fraction of muscle fibers activated, for the three
configurations used in simulations (left, rat plantaris; middle, rat EDL; right, idealized hexagonal array). B:
corresponding values of oxygen deficit. F, Arteriolar response mechanism; E, conducted response mechanism.
* Values corresponding with the cases shown in Fig. 4.
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at high levels of activation, without triggering the
perfusion of additional MVUs. In the conducted response mechanism, it is assumed that perfusion of an
arteriole is determined by PO2 levels adjacent to the
capillaries belonging to the MVU fed by the arteriole.
This mechanism leads to closer matching between perfusion of MVUs and fiber activation, with better control
of the tissue oxygen deficit. The results favor the assumption that conducted responses from capillaries to
arterioles play a role in regulating perfusion of skeletal
muscle. However, the involvement of other mechanisms, including the arteriolar response mechanism,
cannot be ruled out based on the present results.
An important simplification in the model is the assumption of a fixed PO2 level in all perfused capillaries.
According to this assumption, each capillary has two
possible states in the model, unperfused and perfused,
and the rate of blood flow in the capillary does not
otherwise enter into the model. In reality, the PO2 of
each perfused capillary varies along its length, depending on its flow rate and the rate at which oxygen is
extracted from it. The flow rate may vary with the level
of muscle activation. Simulation of such a system is
possible in principle (31) but would add greatly to the
complexity of the model and to the number of arbitrary
assumptions that would be necessary.
One consequence of this simplification is that the
model does not allow quantitative prediction of the
variation of blood flow rate with muscle activation.
Experimental data (15, 35) show an approximately
linear increase in blood flow as a function of contractile
force or oxygen demand. Such a gradual increase would
be difficult to explain if the number of perfused capillaries increased in a highly nonlinear way, as predicted
by Fuglevand and Segal (13). The present model (with
the conducted response mechanism) predicts variation
in the number of perfused capillaries with muscle activation that is qualitatively similar to the reported
experimental variation in blood flow with level of muscle activation, i.e., roughly linear with a positive intercept on the vertical axis. This is consistent with the
experimental data if it is assumed that once a capillary
is perfused, its flow rate remains approximately constant with further increases in muscle activation because overall flow rate is then proportional to the
number of perfused capillaries.
A further simplification in the model is the assumption of a fixed rate of oxygen consumption in active
muscle fibers. In reality, oxygen consumption rates of
muscle fibers can vary depending on the level of activation (28), with a gradual increase from the basal rate
to a maximal rate of consumption (23). Actual variations in fiber oxygen consumption rates may be wider
than the 16-fold variation between resting and active
rates assumed here. Such variations would increase
the spatial heterogeneity in oxygen consumption rates
but would not lead to qualitatively different behavior
from that predicted here.
In conclusion, the model shows that the spatial mismatch between functional units of capillary perfusion
and motor units leads to substantial heterogeneity of
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studies (2, 14, 39) have shown that stimulation of
muscle fibers causes increased blood flow in adjacent
capillaries. The mechanisms of this response are not
known but likely involve a combination of mechanisms
involving potassium, oxygen, adenosine, nitric oxide,
other released metabolites, and/or neural feedback
(16). Responses to oxygen levels probably play a crucial
role. Arterioles are known to respond by constriction or
dilation to changes in tissue oxygen levels (10, 20, 37).
Furthermore, oxygen availability is the most important factor limiting the rate of muscle working in
prolonged exercise, so arteriolar response to oxygen
would provide the most direct feedback mechanism to
match flow with metabolic needs. Control of MVUs was
therefore assumed to depend on oxygen levels in this
model, although other mechanisms, such as responses
to changing extracellular potassium levels, could also
be explored using a similar approach.
The model was used to examine the consequences of
two different assumptions regarding the sites of oxygen sensing in the tissue. In the arteriolar response
mechanism, arterioles were assumed to dilate when
the minimum PO2 level along an arteriole falls below a
threshold level of 5 mmHg. This parameter is difficult
to estimate from available data on arteriolar responses
to oxygen levels. The level of 5 mmHg was chosen to
keep the oxygen deficit within a low range at low and
moderate levels of activation. As already mentioned,
oxygen deficit could not be controlled at higher levels of
muscle activation, even if this threshold was increased.
Similar results were obtained if the average rather
than the minimum PO2 along the arteriole was used as
a criterion, but a higher threshold level was needed.
Although the terminal arterioles are the primary site
for the control of flow in MVUs, they are not necessarily the main sites for sensing of tissue oxygen levels
(19). The conducted response mechanism is based on
the alternative assumption that capillaries can sense
oxygen levels. According to this assumption, low PO2
levels trigger a response that is transmitted to the
arteriole, causing dilation. Evidence for such an information transfer mechanism has been presented by
Tyml et al. (38), and it may involve conducted electrical
responses (32, 34). In the model, perfusion of a feeding
arteriole was assumed to occur when the average capillary PO2 fell to ⬍7 mmHg. This parameter cannot be
estimated directly from available experimental data,
and the assumed value was chosen to keep the oxygen
deficit low over the full range of muscle activation.
The results (Fig. 7) show that the mechanisms regulating MVU perfusion affect the ability of the system
to deliver oxygen as needed despite the spatial mismatch between MVUs and motor units. In the arteriolar response mechanism, it is assumed that perfusion
of a MVU was triggered by a decline in PO2 levels
adjacent to the terminal feeding arteriole. Because this
arteriole typically flows through a region perfused by
capillaries from other MVUs (Fig. 3), it does not necessarily respond to a decline in PO2 in the region of the
MVU that it feeds. As a result, tissue hypoxia is not
well controlled and the oxygen deficit tends to increase
OXYGEN DELIVERY TO SKELETAL MUSCLE FIBERS
oxygen levels in partially activated skeletal muscle.
The relationship between the level of muscle activation
and the fraction of perfused capillaries needed to
achieve adequate tissue oxygenation depends on the
mechanism by which perfusion of MVUs is controlled.
A control mechanism based on the sensing of oxygen
levels by capillaries and transmission of this information to the feeding arterioles via conducted responses
was found to lead to adequate tissue oxygenation over
the full range of muscle activation, with the fraction of
perfused capillaries increasing gradually with increasing activation.
We thank Dr. Fay Hansen-Smith for providing an unpublished
photomicrograph of rat EDL muscle.
17.
18.
19.
20.
21.
22.
This work was supported by National Heart, Lung, and Blood
Institute Grants HL-34555 and HL-70657.
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DISCLOSURES
H963