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This article was downloaded by: [113.210.135.52]On: 18 March 2014, At: 01:59Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Sports BiomechanicsPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/rspb20
Use of deterministic models in sportsand exercise biomechanics researchJohn W. Chow a & Duane V. Knudson ba Center for Neuroscience and Neurological Recovery, MethodistRehabilitation Center , Jackson, Mississippi, USAb Department of Health and Human Performance , Texas StateUniversity , San Marcos, Texas, USAPublished online: 09 Aug 2011.
To cite this article: John W. Chow & Duane V. Knudson (2011) Use of deterministic modelsin sports and exercise biomechanics research, Sports Biomechanics, 10:3, 219-233, DOI:10.1080/14763141.2011.592212
To link to this article: http://dx.doi.org/10.1080/14763141.2011.592212
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Use of deterministic models in sports and exercisebiomechanics research
JOHN W. CHOW1 & DUANE V. KNUDSON2
1Center for Neuroscience and Neurological Recovery, Methodist Rehabilitation Center, Jackson,
Mississippi, USA, and 2Department of Health and Human Performance, Texas State University, San
Marcos, Texas, USA
(Received 14 October 2010; accepted 20 May 2011)
AbstractA deterministic model is a modeling paradigm that determines the relationships between a movementoutcome measure and the biomechanical factors that produce such a measure. This review provides anoverview of the use of deterministic models in biomechanics research, a historical summary of thisresearch, and an analysis of the advantages and disadvantages of using deterministic models. Thedeterministic model approach has been utilized in technique analysis over the last three decades,especially in swimming, athletics field events, and gymnastics. In addition to their applications in sportsand exercise biomechanics, deterministic models have been applied successfully in research on selectedmotor skills. The advantage of the deterministic model approach is that it helps to avoid selectingperformance or injury variables arbitrarily and to provide the necessary theoretical basis for examiningthe relative importance of various factors that influence the outcome of a movement task. Severaldisadvantages of deterministic models, such as the use of subjective measures for the performanceoutcome, were discussed. It is recommended that exercise and sports biomechanics scholars shouldconsider using deterministic models to help identify meaningful dependent variables in their studies.
Keywords: Exercise science, mechanical analysis, performance analysis, quantitative analysis, researchmethodology
Introduction
Advances in computers, transducers, and imaging technologyhavemade it easier andquicker to
collect biomechanics data. Several reviews of these methods in sports biomechanics and their
potential have been reported (Bartlett, 1997; Lees, 2002; Yeadon & Challis, 1994). However,
the increase in the number of laboratories and research reports in sports biomechanics over the
last two decades has not resulted in substantial improvements in the theoretical bases or
frameworks used in sports biomechanics research.
Exercise and sports biomechanics research is a growing field and the expanding body of
research reports fit the chaos in the brickyard perspective (Forscher, 1963) of modern
scientific inquiry, where the danger of an increasing number of less than meaningful
observations are being reported in the literature is a real possibility. Hudson (1997) has
ISSN 1476-3141 print/ISSN 1752-6116 online q 2011 Taylor & Francis
DOI: 10.1080/14763141.2011.592212
Correspondence: John W. Chow, Ph.D., Center for Neuroscience and Neurological Recovery, Methodist Rehabilitation Center,
1350 East Woodrow Wilson Drive, Jackson, MS 39216, USA, E-mail: [email protected]
Sports Biomechanics
September 2011; 10(3): 219233
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noted how our students and colleagues often consider sports biomechanics an atheoretical
and irrelevant discipline. Knudson (2005) reported that fewer than 20% of the papers
published in two applied biomechanics serials could be rated highly on rationale, theory and
statistical analysis. The common use of many statistical tests on many dependent variables in
most exercise and sports biomechanics research reports inflates the experiment-wise type I
error rate (Knudson, 2009) and prevents us from understanding which effects are truly
statistically significant and which are likely to be type I errors.
In many fields of study, a model (a graphical or mathematical description of a system or
process) can be used as a basis for theoretical or empirical understanding of that system or
process. Deterministic models serve such purposes in biomechanics, and their use could
help to promote the use of theoretical models in sports and exercise biomechanics research.
Concise overviews of deterministic models have been given in several review articles
(Glazier, 2010; Lees, 1999, 2002) and textbooks (Bartlett, 1999; Hay & Reid, 1988). This
paper presents a comprehensive narrative review synthesizing the use of deterministic
models in sports biomechanics. First we define deterministic models and summarize their
use in biomechanics. The advantages and disadvantages of this approach are reviewed, and
we conclude with the potential application of these models in research and with athletes.
The deterministic model
A deterministic model is a modeling paradigm that determines the relationships between a
movement outcome measure and the biomechanical factors that produce such a measure
(Hay & Reid, 1988). A block diagram is often used to provide an overview of the
relationship. For example, the goal of a 100-m dash is for a sprinter to complete the distance
of 100m (Figure 1) in the shortest amount of time. This time is determined by the average
speed and the distance covered (a constant in this case) (t D/Savg). The average speed isfurther determined by the athletes average stride length and stride frequency (Savg SLavg SFavg). When necessary, the average flight and support times can be included asfactors that produce the average stride frequency. Stride frequency is determined as the
reciprocal of stride time, which is the sum of the flight and support times during a single
stride. Also, the average stride length can be divided into three shorter distances the
takeoff, flight, and landing distances (Hay, 1993).
Dr. James G. Hay is inarguably the pioneer of deterministic model use in biomechanical
analyses. While working on his dissertation on high jumping (Hay, 1967), he was having
trouble keeping the roles of the variables (performance parameters of high jumping) clear in
his mind, and started to draw block diagrams to clarify things. Hays initial problems with
these block diagrams revolved around causality, inclusion and redundancy. He became
aware that, in some cases, he was leaving an important factor out of a block diagram while in
other cases, he was including factors that were redundant for example, the horizontal
velocity of takeoff, the vertical velocity of takeoff and the angle of takeoff. This eventually led
him to identify a basic mechanical equation that linked the variable in one box to the
variables in the boxes linked to it from below. With this approach, the relationships in Hays
block diagrams were all-inclusive and non-redundant, and all the relationships involved were
causal in nature (Dr. J. Hay, personal communication, May 5, 2001).
According to Hay (1984), a deterministic model should have two distinguishing features.
First, the model is made up of mechanical quantities or appropriate combinations of
mechanical quantities. Secondly, all the factors included at one level of the model must
completely determine the factors included at the next highest level. It is this second feature
that leads us to refer to these types of models as deterministic models. Some authors (e.g.
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Bartlett, 1999; Lees, 2002) refer to these models as hierarchical models. It is worth noting
that the deterministic approach defined here is not the same as the deterministic models in
mathematical modeling. A deterministic model in mathematical modeling is a direct
mathematical representation of phenomena that occur in deterministic, continuous, or
discrete patterns (Kleinstreuer, 1997).
Hay extended the application of the deterministic model by using correlation analysis to
document the strength of association between the movement goal and the subsequent factors
in the model. He and his students illustrated this with papers on the limiting factors of
vertical jumping (Hay et al., 1976, 1978, 1981). These studies were some of the first to use
partial correlation and multiple regression to account for intercorrelations between variables
and identify biomechanical variables with unique associations with performance. The
deterministic model combined with the large sample of subjects allowed the identification of
key joint torques contributing to jump height. Hip extensor torques early in propulsion
and shoulder extensor torques near take-off were identified as significant determinants.
Figure 1. Model for the 100-m dash and illustration of selected kinematic characteristics of a running stride.
Use of deterministic models 221
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The mechanisms of these benefits have recently been confirmed by experimental and
simulation studies (Cheng et al., 2008; Domire & Challis, 2010; Feltner et al., 1999).
Replication of correlational studies or experimental/modeling verification is important
because causation cannot be inferred from correlations and cross-validation of these
associations is necessary.
Development of deterministic models
The steps in the development of a deterministic model are described in detail by Hay and
Reid (1988). Briefly, the first step is to identify the primary goal, result/outcome of the
performance to be investigated. The outcome of a performance can be an objective measure
(e.g. distance, height, time, etc.) or a subjective measure (e.g. points awarded in gymnastic
and diving competition). The next step is to identify those factors that produce the result. As
stated earlier, the factors included in the model should normally be mechanical quantities
wherever possible and each factor should be completely determined by those factors that are
linked to it from below.
It should be emphasized that it is possible to develop more than one model for movement
tasks of similar results. The discus throwmodels with the speed of release of the discus as the
performance result developed by Hay and Yu (1995) and Chow and Mindock (1999) can be
used to illustrate this point. In the second level of the model used by Hay and Yu (Figure 2), a
thrower loses distance if the discus is released inside the throwing circle and vice versa. In the
third level, the flight distance is determined by factors governing the trajectory of a projectile.
In the next level, Hay and Yu considered the speed of the discus at the instant of release to be
the sum of changes in the speed of the discus during different phases of a throw. As a result,
the terminal factors (boxes at the ends of the various paths) of the model are the distance loss,
Figure 2. Model for the discus throw used by Hay and Yu (adapted from Hay & Yu, 1995).
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angle and height of release, aerodynamic distance, and the changes in discus speed during
different phases of a discus throw.
The model developed by Chow and Mindock (1999) focused on the kinematic
characteristics of upper body segments during throws performed by wheelchair athletes
(Figure 3). The first three levels of the model are similar to those of Hay and Yu (1995), while
the rest of the model is formed by repeated applications of several equations relating
kinematics of distal endpoint to proximal endpoint of a segment of the throwing arm. The
terminal factors of the model can be categorized into three groups: (1) the characteristics of
the discus at the instant of release, (2) the characteristics of different upper body segments at
the instant of release, and (3) the characteristics of different segments during the forward
Figure 3. Model for the wheelchair discus throw used by Chow and Mindock (1999).
Use of deterministic models 223
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swing. Apart from the common finding that the speed of release is the most influential
determinant of the distance of the throw, there are differences in influential variables between
able-bodied and disabled discus throwers. Hay and Yu (1995) demonstrated the importance
of achieving a large gain in the speed of the discus during the second double support phase in
elite able-bodied discus throwers, while Chow and Mindock (1999) found the shoulder
girdle movement during the forward swing to be the important determinant of both medical
classification and throw distance of wheelchair athletes. Although the movement tasks of
able-bodied and wheelchair discus throws are not exactly the same, the segmental approach
used in wheelchair discus can by applied in future research to the delivery phase of the able-
bodied discus throw.
Use of deterministic models in biomechanics
Over the years the utility of a deterministic model approach in biomechanical research has
been illustrated in several sports, especially in swimming, athletics field events, and
gymnastics. A concise summary of this research is presented in Table I.
Use of deterministic models has clarified key performance parameters in swimming starts
and strokes. In competitive swimming the average speed (S) is the product of the average
stroke frequency (SF ) and average stroke length (SL) and the relationships between these
parameters have been investigated using swimmers of different performance levels. Craig
and Pendergast (1979) asked college swimmers to swim at different speeds and found that
increased S toward the maximum was achieved by a combination of increasing SF and
decreasing SL in all of the four competitive strokes. In a group of 168 untrained high school
students, improvement in breaststroke S after six weeks (three times/week) of training
depended upon an increase of SL, rather than SF (Saito, 1982). Based on data collected at
the 1982 British Commonwealth Games, Pai et al. (1984) concluded that elite swimmers
achieved very similar S with very different combinations of SL and SF. With the aid of a
deterministic model Grimston and Hay (1986) identify 21 anthropometric variables relevant
to success in swimming and tried to relate these variables to the freestyle swim performance
of college swimmers. The axilla cross-sectional area, a variable that could be substantially
affected by training, was found to have the largest influence on both SL and SF.
Using the total starting time (sum of block, flight, and water times) as the performance
goal of the hands-between-the feet grab starting technique, Guimaraes and Hay (1985)
tested 24 male high school swimmers and identified several mechanical characteristics that
contribute to a faster start. McLean et al. (2000) adapted the model by Guimaraes and Hay
(1985) to compare the kinematics of three types of relay start one or two-step approach,
and a no-step start. Their findings suggested that step starts offered some performance
improvements over the no-step start.
Deterministic models have been successfully used in the study of jumps and throws in
track and field athletics. Using the deterministic model approach Hay and colleagues
(1985a, 1985b, 1986) successfully identified mechanical characteristics that are significantly
related to the official distances of long and triple jumps of elite jumpers. Chow and Hay
(2005) developed a model of the last support phase of the long jump and used it to examine
the interacting roles played by the approach velocity, the explosive strength (represented by
vertical ground reaction force), and the change in angular momentum about a transverse axis
through the jumpers centre of mass during the last support phase of the long jump, using a
computer simulation technique. The results indicated that approach velocity and vertical
ground reaction force are not independent factors in determining jump distance, and the
jump distance was over-estimated if the change in angular momentum was not considered in
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TableI.Summary
ofresearcharticlesusingthedeterministicmodelapproach.
Reference
Subjects
Perform
ance
result
Terminalfactors
Statistical
approach
Key
findings
Hayetal.(1976)
213M
Verticaljump
height
Jointanglesandkinem
atics
ofcenterof
gravity(C
G)andlimbsegments
Partial
CORR&
REG
Theactionsofhead,trunk,andarm
s
contributedsignificantlyto
thevari-
ationsin
CG
elevationfrom
takeoffto
peakofflight.
Hayetal.(1978)
213M
Verticaljump
height
Jointangularim
pulses
Partial
CORR
Torques
attheshoulder,hip,andknee
weresignificantcontributorsto
jumpheightandcontributionsvaried
acrossphases.
Craig&Pendergast(1979)
63M,47F
Averagesw
im-
mingspeed(S)
Averagestrokelength
(SL)andstroke
frequency
(SF)
t-test
WithinsubjectSincreasedasaresultof
increasingSFanddecreasingSL.
Hayetal.(1981)
194M
Verticaljump
height
Meanjointtorques
REG
Ten
shoulder,hip,knee,andankle
torques
weresignificantcontributorsto
jumpheightandcontributionsvaried
acrossphases
Saito(1982)
168M
high
schoolstudents
Sofbreast-
stroke
SLandSF
t-test
Improvem
entin
Safter
sixweeksof
training(3x/week)wasdueto
an
increase
inSF,rather
thanin
SL.
Paietal.(1984)
64M,46F
Soffourcom-
petitivestrokes
SLandSF
CORR&
REG
Swasnotsignificantlycorrelatedwith
either
SLorSF.Elitesw
immersused
differentcombinationsofSLandSFto
achieve
afairlyconstantS.
Guim
araes
&Hay(1985)
24M
high
schoolsw
im-
mers
Swim
grab
starttime
CG
kinem
atics
andkineticvariables
determinetheblock,flight,&water
times
CORR&
REG
Forafaster
startsw
immersshould
(a)
moveCG
fastforward
onblock,(b)
maxim
izebackward
forcebyfeet,&(c)
maxim
izeforcebyhandsinforward
and
upward
direction.
Hay&Miller(1985a),Hay
etal.(1986)
12M
&12F
elitelongjum-
pers
Long
jumpdistance
Velocities
attakeoffandtouchdownof
thelastfourstrides
oftheapproach
and
thevelocity
andangleattakeoff
CORR
Confirm
ingthedominantrolesofthe
horizontalvelocityoftheapproach,the
horizontalandresultantvelocities
at
takeoff,andtheflightdistance.Other
factorscloselyrelatedto
the
jumpdistance
wereidentified.
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TableIcontinued
Reference
Subjects
Perform
ance
result
Terminalfactors
Statistical
approach
Key
findings
Hay&Miller(1985b)
12M
elitetriple
jumpers
Triple
jumpdistance
Velocitiesattakeoffandtouchdownand
times
offlightandsupportforthethree
phasesofthetriplejump
CORR
Themore
thejumpersresources
are
expended
priorto
thejumpphase
and
themore
verticaltheeffortattakeoff
intothejump,thebetterthefinalresult.
Grimston&Hay(1986)
12M
college
swim
mers
Averagesw
im-
mingspeed(S)
SLandSF.Adeterministicmodelwith
swim
timeastheresultwasusedto
identifyanthropometricvariablesrel-
evantto
successin
swim
ming
Partial
CORR&
REG
Theanthropometricvariables
accountedfor89%
(SL),41%
(SF),
and17%
(S)ofthevariancesin
the
measuredcharacteristics
oftheir
strokes.AlthoughSislittleinfluenced
bythephysique,thecombinationofSL
andSFusedto
attain
agiven
Sisvery
much
afunctionofsw
immersphysi-
que.
Wilsonetal.(1987)
24M
&10F
Skatingsprint
speed
Stridelength,stridefrequency,body
segmentanglesandrangeofmotion
duringsinglesupport
CORR&
REG
Sprintskatingspeedisassociatedwitha
longstridelength
andalargesingle-
supportdistance.
Takei(1988;1989;1990;
1992;1998),Takei&Kim
(1990),Takeietal.(1992;
2000;2003)
Ranged
from
24
to122M/F
worldclass
gymnasts
Gymnastic
vault:point
awarded
by
judges
Linearandangularmotionofthe
gymnastin
preflight,postflight,andthe
executionduringthevault
CORR
Mechanicalfactorsassociatedwith
judgesscoreswereidentified
for
differenttypes
ofvaults.
Gervais(1994)
1gymnast
Gymnastic
vault:judges
score
Tim
eonhorse,timeofpostflight,CG
locationandvelocities
postflight,and
pre-andpost-flightangularmomentum
values
CORR
Theresultsdem
onstratedthatthe
optimizationapproach
developed
could
produce
aviablepredictionofan
individualsoptimalperform
ance
ofa
handspring11 2frontsaltolonghorse
vault.
Hay&Yu(1995)
14M
&15F
Discusthrow
distance
Changes
inthespeedofthediscus(Ds)
duringdifferentphases,speed,angle,
andheightofrelease
CORR
Dsduringtheseconddoublesupport
phase
andthespeedofrelease
are
influentialdeterminantofthethrow
distance
Dixon&Kerwin
(1998)
3F
Maxim
um
Achillesten-
donforce
Componentsofgroundreactionforce
(GRF)andcenterofpressure,and
digitized
marker
location
ANOVA
Thefindingthatincreasedheelliftsmay
increase
maxim
um
Achillestendon
forcesuggestedthatcautionisadvised
intheroutineuse
ofthisintervention.
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TableIcontinued
Reference
Subjects
Perform
ance
result
Terminalfactors
Statistical
approach
Key
findings
Chow&Mindock
(1999),
Chowetal.(2000;2003b)
1417M
wheelchairath-
letes
Discus,shot
put,&javelin
measureddis-
tance
Kinem
atics
oftheim
plementand
differentupper
bodysegmentsatthe
instantofrelease,andkinem
atics
of
differentsegmentsduringthedelivery
CORR
Inadditionto
thespeedofthe
implementatrelease,im
portantdeter-
minantsofmedicalclassificationand
measureddistance
wereidentified
for
each
fieldevent.
McL
eanetal.(2000)
10M
college
swim
mers
Swim
start
time
Speed,angle,andbodypositionat
takeoff,takeoffandentryheights,and
airbornebodymomentofinertiaand
angularmomentum
ANOVA
Comparedwithno-stepstarts,
increasedhorizontaltakeoffvelocity,
decreasedverticaltakeoffvelocity,
increasedtakeoffheight,steeper
entry
angleandorientationwerefoundin
step
starts.
Powers&Harrison(2002)
8show-jumping
horses
CG
path
duringflight
CGvelocitiesattakeoffandlandingand
CG
elevationduringflight
ANOVA
Theriderseffectonjumpinghorseswas
primarilydueto
behavioralchanges
in
horsesmotion,rather
thaninertial
effects.
Chowetal.(2003a)
4M,4F,pro-
fessionalplayers
Balllocationat
landingfora
tennisserve
Kinem
atics
ofballtoss,pre-andpost-
impactballandracquetvelocities
Wilcoxon
From1stto2ndserveplayerstossed
the
ballcloserto
thebodyandim
parted
spinontheballbychangingtheracquet
verticalandlateralvelocities.
Chow&Hay(2005)
NA(computer
simulation)
Long
jumpdistance
Approach
velocity,verticalGRF
(VGRF),andchangein
angular
momentum
duringtakeoff
NA
Sensitivityanalysisrevealedthat
approach
velocity
andVGRFare
not
independentfactorsin
determiningthe
jumpdistance.
Leighetal.(2008)
51M,53F
Discusthrow
distance
Hip-shoulder
andshoulder-arm
separ-
ation,trunkforward-backward
tilt,
throwing-arm
elevationangles,and
throwingprocedure
phase
times
CORR&
REG
Fem
alethrowersuse
amore
sophisti-
catedtechniquethanmalethrowers.
Malethrowersmay
place
more
reliance
onphysicalstrength
toachieve
long
distances.
Abbreviations:M:male,F:female,CORR:correlationanalysis,REG:regressionanalysis,ANOVA:analysisofvariance,NA:notapplicable.
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the analysis. In addition to horizontal jumps, Hay and Yu (1995) developed a model to
analyse discus throws performed by elite able-bodied athletes (Figure 2). In separate studies
Chow and colleagues (Chow et al., 2000, 2003b; Chow & Mindock, 1999) applied a
stationary throw model to the analyses of shot put, discus throw and javelin throw
performance of wheelchair throwers of different medical classifications (Figure 3).
The models used in Takeis studies on gymnastic vaults are good examples of models that
use subjective measures for the performance outcome (Figure 4). Takei and colleagues have
used deterministic models to guide their biomechanical analyses of several gymnastic vaults
performed by elite gymnasts (Takei, 1988, 1989, 1990, 1992, 1998; Takei & Kim, 1990;
Takei et al., 1992, 2000, 2003). Figure 4 shows a typical model used by Takei. Studies using
these models and correlation analysis have documented influential performance variables in
gymnastic vaults and key techniques that are significantly associated with successful
performance (points awarded by judges). Instead of statistical approaches commonly used
by others, Gervais (1994) utilized the evaluation scheme (point deductions) of a vault in
conjunction with a deterministic model to set up an optimization process for predicting the
optimal performance of a gymnastic vault. The predicted optimal performance was found to
display greater virtuosity in postflight height, distance and angular momentum when
compared with the individuals best trial performance.
Other sports skills studied using the deterministic model approach are roller skating
(Wilson et al., 1987), horse jumping (Powers & Harrison, 1999, 2002) and tennis serve
(Chow et al., 2003a). Deterministic models were also used in reviews analyzing the slalom in
alpine skiing (Bober, 1996) and rowing (Soper & Hume, 2004), and physical training for
increasing vertical jump height (Ham et al., 2007).
Deterministic models can be adapted to a goal to minimize the exposure to a mechanical
variable that is hypothesized to be the primary cause of injury. Dixon and Kerwin (1998)
Figure 4. Model showing preflight factors causally related to the official score of a handspring vault (adapted from
Takei, 1989).
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reported one of the few studies that have explicitly taken advantage of deterministic models
to study influential factors related to injury. It is possible that the use of deterministic
models in conjunction with multivariate statistical analysis can identify factors and their
strength of association with injury rates.
Use of deterministic models has found its way into other exercise and sports science
research utilizing biomechanical data. Although no block diagrams were used, three studies
on the acquisition of motor skills have used deterministic models (Heise & Cornwell, 1997;
Schneider et al., 1989; Yoshida et al., 2004). Schneider et al. (1989) examined the net joint
moments at the upper extremity joints during a maximum speed hand movement, in a
vertical plane up and around a barrier to a target. Their model focused on the three
components of the net joint moment: gravitation, interactive and generalized muscle
moments. Their results supported Bernsteins (1967) hypothesis that practice alters motor
coordination among muscular and passive joint moments. Using the same mathematical
procedures Heise and Cornwell (1997) and Yoshida et al. (2004) tried to determine, for a
planar multi-joint throwing skill and a target reaching task respectively, whether the relative
contributions of the components of the net joint moment at the elbow and shoulder change
after an intervention. With practice, subjects in the Heise and Cornwell (1997) study could
throw further. However, the relative contribution of net joint moment components remained
unchanged. Results from Yoshida et al. (2004) suggest that rapid aiming movements are
controlled through a reciprocal interplay between intersegmental dynamics during the
acceleration phase and error corrections. It is clear that deterministic models have been
useful in conducting biomechanical research on a wide variety of human movements. It
should also be mentioned that some studies used the deterministic modeling approach but
the approach was not explicitly stated [e.g., Yu et al. (2006) and Zablotny et al. (2003)].
Extension of deterministic models to qualitative biomechanics
Besides their utility in planning and analyzing biomechanical data in research, Hay also
advocated that deterministic models be used as a basis for qualitative analysis of sports
skills (Hay, 1984; Hay & Reid, 1988). There is strong logical support for this position
because these models enable coaches to focus on important biomechanical variables that
directly affect the movement goal. Some coaches are not educated in exercise and sports
science and rely on passed-down craft knowledge of sports techniques. Qualitative analysis
of technique decisions on meaningful biomechanical factors that directly affect
performance is important, so use of deterministic models to guide qualitative analysis
could be an improvement on traditional error detection and correction based on unverified
technique beliefs.
The utilization of deterministic models as a guide for qualitative analysis, however, has not
been tested by research and deterministic models are only one of several approaches
(Knudson & Morrison, 2002). Hudson (1997) has been critical of any qualitative analysis
model that does not focus the attention of the analyst and athlete on kinematic variables that
are visually observable and potentially meaningful in modifying technique, while others
encourage use of deterministic models and kinetic variables in qualitative analysis (Sanders,
2004). There has been limited and fragmented research on the interdisciplinary skill of
qualitative analysis of human movement (Knudson & Morrison, 2002), so there is a lack of
evidence as to which approach to qualitative analysis is best or the efficacy of biomechanical
data in improving sport performance (Lees, 1999). There is a need for research comparing
the use of deterministic models of qualitative analysis with other models of qualitative
analysis.
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Advantages and disadvantages
The primary advantage of using deterministic models is to help to avoid selecting
performance variables arbitrarily (the trial and error approach). The deterministic model
approach is a more objective approach to identifying factors that affect the outcome of a
performance. If done correctly, this ensures that no major factor that determines the
outcome is overlooked and that nothing is included unnecessarily (Hay, 1984). Use of
deterministic models in biomechanical research could reduce the problems caused by
numerous dependent variables noted earlier.
Another advantage of the deterministic models is that it can be used to provide a theoretical
basis (mechanical relationships) for statistical modeling (Bartlett, 1999). For example,
referring to the model depicted in Figure 3, the significant correlations between the range of
motion and average angular velocity of the shoulder girdle during the forward swing and the
measureddistance (r $ 0.72) of throwers allowed the investigators to affirm the significance ofshoulder girdle movement in wheelchair discus throw (Chow &Mindock, 1999).
It is not uncommon to see many factors and levels of factors in a well-developed model.
A major concern when using such a model for statistical modeling is the sample size and
assumptions of the statistics used. A reasonably large sample of subjects and trials is needed
in order to come up with an acceptable power value. For example, to allow a reliable
multiple linear regression analysis and to overcome problems of colinearity, Hay et al.
(1981) tested 194 subjects for the purpose of identifying limiting factors of vertical
jumping. Partial correlation and multiple regression analyses should be used to define the
variables that are meaningful in predicting the goal of the movement, thereby eliminating
variables that are intercorrelated or not truly influential. Care must also be taken to ensure
and report that the scatterplots do not violate assumptions of linearity and random error, so
that the strength of the correlations and regression equations accurately model the data.
Subjectivity in selecting the number of levels and variables in a deterministic model can be
a disadvantage at times. For example, increasing the number of variables expands the study,
but imposes greater demands on sample size and interpretation. In any event, it is
recommended that researchers should strive to minimize the number of variables involved
and statistical tests performed to maximize the power of their analysis.
Summary
The deterministic model approach provides a strong theoretical or mechanical basis for
examining the relative importance of various factors that influence the outcome of a
movement task. These models have been used successfully in research on a wide variety of
motor skills in the last four decades. Studies using deterministic models in biomechanics and
motor behaviour illustrate their utility in identifying critical mechanical parameters in
humanmovement. The use of correlation and regression analyses to document the size of the
association of variables influencing movement is an important step in planning prospective
studies to apply biomechanics to improve movement performance or reduce injury risk.
Despite the success of these models in a wide variety of biomechanics research, most of the
scholars using deterministic models have links to Dr. Hay and his students. This somewhat
limited use of deterministic models in research may be because many associate deterministic
models with qualitative biomechanical analysis advocated by Hays classic texts (Hay, 1993;
Hay & Reid, 1988). While deterministic models logically have the potential to improve
qualitative analysis, biomechanics scholars are encouraged to use deterministic models to
improve the focus and impact of their research.
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It is likely that greater use of deterministic models in planning biomechanics research can
help reduce some of the problems in the literature related to numerous and likely
meaningless dependent variables (Hudson, 1997; Knudson, 2005, 2009). Research can then
be focused on variables with a strong theoretical or mechanistic connection to performance
as well as risk of injury.
We recommend that sports biomechanics scholars consider using deterministic models to
help identify meaningful dependent variables in their studies, and build mechanistic or
theoretical linkages related to the independent variables being studied. When correlation and
regression analyses are used in conjunction with a deterministic model, care must be take to
sample a well-defined population of subjects adequately in order to document the magnitude
of influence of the factors on performance or potential injury. For scholars interested in the
application of biomechanical theory and principles, research comparing deterministic
models of qualitative analysis with other models would be beneficial to the field.
Acknowledgements
The preparation of this review was supported in part by the Wilson Research Foundation
(Jackson, Mississippi, USA).
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