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Modeling: optimal marathon performance
on the basis of physiological factors
MICHAEL J. JOYNER
Department of Anesthesiology, Mayo Clinic and Mayo Foundation, Rochester, Minnesota 55905
JOYNER, MICHAEL J.
Modeling: optimal marathon perfor-
mance on the basis
of
physiological factors.
J. Appl. Physiol.
70(Z): 683-687, 1991.-This paper examines current concepts
concerning “limiting” factors in human endurance perfor-
mance by modeling marathon running times on the basis of
various combinations of previously reported values of maximal
0, uptake (VO,,, ) lactate threshold, and running economy in ,
elite distance runners. The current concept is that vo2,, sets
the upper limit for aerobic metabolism while the blood lactate
threshold is related to the fraction of vo2 max that can be sus-
tained in competitive events greater than -3,000 m. Running
economy then appears to interact with \io, max and blood lac-
tate threshold to determine the actual running speed at lactate
threshold, which is generally a speed similar to (or slightly
slower than) that sustained by individual runners in the mar-
athon. A variety of combinations of these variables from elite
runners results in estimated running times that are signifi-
cantly faster than the current world record (2:06:50). The fast-
est time for the marathon predicted by this model is 15758 in a
hypothetical subject with a VO, 1118X of 84 ml
l
kg-‘. min-‘, a lac-
tate threshold of 85% of VO 2 max, and exceptional running econ-
omy. This analysis suggests that substantial improvements in
marathon performance are “physiologically” possible or that
current concepts regarding limiting factors in endurance run-
ning need additional refinement and empirical testing.
maximal oxygen uptake; lactate threshold; running economy;
human performance
PHYSIOLOGISTS
have long been interested in modeling
optimal human performance in various running events
on the basis of world records (23,26). Although a variety
of approaches to this problem has been used (23, 26),
recent mathematical models of running performance
have been improved by the recognition that maximal 0,
uptake
(90,
,,)
cannot be sustained in competition for
S-10 min (23,26). This approach is supported by experi-
mental data demonstrating that submaximal variables
including the blood lactate threshold and running econ-
omy (0, cost to run a given speed) are powerful predic-
tors of endurance running performance (3-5, 7,
11, 14,
16, 22, 25). Along these lines, this paper attempts to ex-
tend the current models of human distance running per-
formance by considering how
VO,
m8X, blood lactate
threshold, and running economy interact as determi-
nants of performance in the marathon.
The emerging concepts concerning the limits of mar-
athon performance are that
vo2
max sets the upper limit
for aerobic metabolism and that the blood lactate thresh-
old is related to the fraction of
Vo2max
that can be sus-
tained in competitive events of 2-3 h. Running economy
then appears to interact with
Vo2mar
and blood lactate
threshold to determine the actual running speed at lac-
tate threshold, which is generally a speed similar to (or
slightly slower than) that sustained by individual run-
ners in the marathon (14).
With this information as a background, the purpose of
this paper is to estimate an “optimal” human perfor-
mance in the marathon on the basis of the following sim-
ple physiological model
marathon running speed
.
=
vo
2 max (ml
l
kg-l
l
min-‘)
X %802 max
at LT
X
RE [km
l
h-l
l VOW’
(ml
l
kg-l . min-‘)I
where LT is lactate threshold, RE is running economy,
and
VO,
is 0, uptake. This model is then used in conjunc-
tion with a range of well-accepted values for these vari-
ables in elite male distance runners to estimate the physi-
ologically optimal marathon performance.
METHODS
Previously reported values for
VO,
max, lactate thresh-
old, and running economy in highly trained and elite en-
durance athletes were used to establish three estimates
(low, average, and high) for each of the three variables.
These values were used in different combinations to esti-
mate the running speed at lactate threshold.
Maximal O2 Uptake
The
VO
2 max values from Pollock’s study (24) of 19 elite
runners were used. These ranged from 71.3 to 84.4
ml
l
kg-l
l
min-l and averaged 76.9 ml
l
kg-’
l
min-‘. On
the basis of these data, the low, average, and high
vo2 max
values used for predictions of running speed at lactate
threshold were 70,77, and 84 ml. kg-l. min-‘. It is recog-
nized that there have been occasional reports of
Vo2max
values >84 ml
l
kg-‘. min-’ in humans; however, this
value is at or near the upper limit of values usually re-
ported for elite runners in textbooks (1). The 70
ml
l
kg-‘. min-l value used for the lower limit was se-
lected
1)
so that symmetrical changes in
VO,
mru among
the low, average, and high values would occur and 2)
because there have been reports of a marathon world
record holder with a
VO
2 m8X value of ~70 ml
l
kg-’
l
min-l
6, 24).
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