Research Article Modeling the Responses to Resistance ... · Research Article Modeling the Responses to Resistance Training in an Animal Experiment Study AntonyG.Philippe, 1 GuillaumePy,

Research ArticleModeling the Responses to Resistance Training inan Animal Experiment Study

Antony G Philippe1 Guillaume Py1 Franccedilois B Favier1 Anthony M J Sanchez2

Anne Bonnieu1 Thierry Busso3 and Robin Candau1

1 INRA UMR866 Dynamique Musculaire et Metabolisme Universite de Montpellier 34000 Montpellier France2Departement STAPS Laboratoire Europeen Performance Sante Altitude Universite de Perpignan EA 4604Via Domitia 66120 Font-Romeu France3Laboratoire de Physiologie de lrsquoExercice Universite de Lyon 42000 Saint-Etienne France

Correspondence should be addressed to Antony G Philippe antonyphilippeuniv-montp1frand Robin Candau robincandauuniv-montp1fr

Received 16 October 2014 Accepted 26 December 2014

Academic Editor Heide Schatten

Copyright copy 2015 Antony G Philippe et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The aim of the present studywas to test whether systemsmodels of training effects on performance in athletes can be used to explorethe responses to resistance training in rats 11 Wistar Han rats (277plusmn 15 g) underwent 4 weeks of resistance training consisting inclimbing a ladder with progressive loads Training amount and performance were computed from total work and mean powerduring each training session Three systems models relating performance to cumulated training bouts have been tested (i) witha single component for adaptation to training (ii) with two components to distinguish the adaptation and fatigue produced byexercise bouts and (iii) with an additional component to account for training-related changes in exercise-induced fatigue Modelparameters were fitted using amixed-effectsmodeling approachThemodel with two components was found to be themost suitableto analyze the training responses (1198772 = 053 119875 lt 0001) In conclusion the accuracy in quantifying training loads and performancein a rodent experiment makes it possible to model the responses to resistance training This modeling in rodents could be used infuture studies in combination with biological tools for enhancing our understanding of the adaptive processes that occur duringphysical training

1 Introduction

Adaptations to training are related to the amount of work per-formed during the exercise sessions The sum of these inputsyields increases and decreases in performance capacitybecause both adaptation and fatigue are produced by exercisebouts Systemsmodels have been developed to quantify theseantagonistic effects of physical exercise on human perfor-mance In 1975 Banister et al [1] proposed the first and mostfrequently used model which includes two components inorder to distinguish the adaptations and fatigue that occurwith training A simplermodel with only one component wasalso proposed to analyze the biological responses inducedby endurance training [2] The most complex model is anextension of that proposed by Banister et al in which the

response to a single exercise depends on past training [3]Using suchmodels with data from animal experiments wouldoffer the opportunity to go beyond the simple quantificationof the relationship between the amount of exercise trainingand performance and would thereby improve our knowledgeabout the nature of the adaptive processes that take placeduring training

Modeling training effects in rodents presents severaladvantages over models in athletes Animal models allow themeasurement of training effects for a broad range of trainingsituations loads and intensities which would be unethical inathletes Moreover the training load and performance can becontrolled with high precision especially in the context ofresistance exercise (RE) on a climbing ladder This precisionenables researchers to capture small details of the training

Hindawi Publishing CorporationBioMed Research InternationalVolume 2015 Article ID 914860 7 pageshttpdxdoiorg1011552015914860

2 BioMed Research International

process and ultimately to optimize the structure of themodel itself Rodent models authorize greater invasivenessyield more biological information and therefore providegreater insight into the adaptive processes that occur dur-ing training particularly regarding the link between theadaptive cell mechanisms and training effects In additionthe animal model could reduce the sources of variability inresponse to training compared with a human model Theinterindividual variability is naturally decreased in animalswith the same genetic background Obviously parametersexternal to training (nutrition sleep quality fatigue related toactivities other than training etc) are controlled in animalsas opposed to humans This homogeneity in the responses tophysical exercise in animals allows us to take advantage ofmixed-effects modeling to analyze the responses of a groupof animals taking interindividual variability into consider-ation When repeated measurements are made on severalrelated statistical units mixed-effects modeling allows amore robust estimation of model parameters than using onlyavailable individual data [4ndash6] The single-individual modelhas generally been used in human studies with the exceptionof onework inwhich themixed-effectsmodelwas applied to agroup of elite swimmers [7]

Among the training programs RE is particularly suitablefor animal studies because RE is associated with high gains inperformance muscle strength and muscle fiber cross-sectional area RE is characterized by exercise performedbetween 60 and 80 of the maximum load and severalexperimentalmodels have been developed to evaluatemuscleand physical performance in response to RE In rats vol-untary exercise based on ladder climbing activity has beenshown to induce muscle hypertrophy changes in muscletypology and increased force and power output [8] One ofthe first studies using ladder climbing as amodel of resistancetraining [9] showed that after 26 weeks of resistance trainingthe trained rats were able to climb 40 cmwhile carrying up to140of their bodymass without changes in the ratio betweenbody andmuscle (EDL and soleus) mass in comparison withcontrolsMore recently we found that rats could climb 1meterwhile carrying 150 of their body mass after 4 weeks ofresistance training in associationwith hypertrophy of 48 offiber IIx in FDP muscle [10] After 8 weeks the rats could liftup to 210 of their body mass Another study [11] demon-strated a 287 increase in the maximal amount of bodyweight that the animals could carry after 8 weeks of training(3 sessions a week)

REmodel offers the opportunity to quantify both trainingwork and performance in animal with a great accuracyThusthe twofold aim of the present study was to (i) test whetherthe systems models used to describe the training response inathletes could be applied in rats and (ii) verify the applica-bility of the mixed-effects model in animals with the samegenetic background in order to improve the statisticalstrength of the training response model

2 Methods

21 Animals and Experimental Design

211 Ethics Statement This study was approved by the Com-mittee on the Ethics of Animals Experiment of Languedoc

Table 1 Change in additional loads lifted by rats during the trainingprogram

Training sessions Load ( body mass) Mean load plusmn SD (g)1 to 5 50 1438 plusmn 1026 80 248 plusmn 2017 and 8 100 3126 plusmn 2469 to 13 120 3971 plusmn 34714 to 16 130 4509 plusmn 37817 and 18 140 4975 plusmn 41619 150 5397 plusmn 476

Roussillon in accordance with the guidelines from the FrenchNational Research Council for the Care and Use of Labora-tory Animals (permit number CEEA-LR-1069)

212 Animal Model Eight-week-old Wistar Han rats (277 plusmn15 g 119899 = 11) obtained from Charles River Laboratories(LrsquoArbresle Rhone France) were housed at a constant roomtemperature and humidity and maintained in a 12 12 h light-dark cycle They had access to standard rat chow (A04Scientific Animal Food amp Engineering Augy France) andwater ad libitum

213 Resistance Training Protocol The rats underwent 4weeks of progressive resistance training The exercise con-sisted of climbing a 1-meter-high homemade ladder inclinedat 85∘ ten times The ladder was adapted from the apparatusof Lee et al [12] Training sessions were held in the afternoonfive times aweekA cloth bag containingweightswas attachedto the base of the tail with tapeThree days before training therats were familiarized with the apparatus by climbing it twicewith 50 of body weight In accordance with the protocolproposed by Begue et al [10] the initial weight attached tothe tail was 50 of the rat body weight and was increasedprogressively until 150 after 4 weeks (Table 1) Each trainingsession consisted in one set of 10 repetitions with 2minrest between trials All rats were able to perform ten climbsper training session Rats from the same cage were trainedtogether Precisely rats were placed on a platform on the topof the ladder and one of them was put on the floor at the baseof the ladder The working rat quickly joined its congenersspontaneously

22 Training and Performance Quantification Training work(TW in J) was calculated as the potential work developedduring the training sessions

TW = (119898load + 119898rat) sdot 119892 sdot Δℎ sdot 119873 (1)

where mass (119898) is expressed in kg 119892 is the constant of thegravity on earth expressed in msdotsminus2 ℎ is the distance climbedin m and119873 is the number of repetitions

Performance was the power output developed during thefull climbing session computed as the work done against

BioMed Research International 3

gravity (TW) divided by total climbing time (s) and expressedin W

Performance = TWtime

(2)

Each climb generally lasted between 3 and 25 s dependingon the load carried by the rats

23 Modeling of the Training Effects

231 Basic Frameworks Since the original work of Banisterand coworkers [1] systemsmodeling has been used to analyzethe adaptations to physical training in subjects enrolled incontrolled experiments or in athletes in real-life situations[13 14] This approach considers the body as a system whoseoutput is the performance varying with the amounts of train-ing ascribed to input Systems theory allows the analysis of adynamical process using abstraction from mathematicalmodels A system is characterized by at least one input andone output and the system behavior is characterized by atransfer function 119867(119905 120579) relating output at a given time toprevious inputs Assuming the formulation of the transferfunction the set of parameters characterizing a subjectrsquosbehavior (noted 120579) is estimated by fitting the model output tothe actual data The number of parameters which can beintroduced in the model is limited by the precision of thedata that can be collected to quantify training input and per-formance output An analysis of the goodness-of-fit is neededto test the statistical significance of the model especially tocompare models differing in complexity that is the numberof equations and related parameters giving the degrees offreedom of the competing models (df)

The transfer function 119867(119905 120579) gives the model perfor-mance at time 119905 by using the product of convolution asfollows

119901 (119905) = 119901 (0) + 119908 (119905) lowast 119867 (119905 120579) (3)

where 119901(0) is the initial performance and the product ofconvolution is defined by

119908 (119905) lowast 119867 (119905 120579) = int

119905

0

119908 (119904) sdot 119867 (119905 minus 119904 120579) 119889119904 (4)

The discretization of (2) gives

119901 (119899Δ119905) = 119901 (0) +

119899minus1

sum

119894=1

119908 (119894Δ119905) sdot 119867 ((119899 minus 119894) Δ119905 120579) (5)

where 119905 = 119899Δ119905 and 119908(0) is assumed to be equal to 0 Fixingthe value of Δ119905 to 1 day led us to consider 119908(119905) as a discretefunction that is a series of impulses each day 119908119894 on day 119894and the product of convolution as a summation in which themodel performance119901119899 on day 119899 is estimated bymathematicalrecursion from the series of 119908119894 before day 119899

232 Systems Models The most often used model initiallyproposed by Banister et al [1] is named Model-2Comp in

Time

Performance

0

0

Positivecomponent

Negativecomponent

k1

k2

tn tg

k1 minus k2

pg

Figure 1 Schematic representation of the response to 1 unit oftraining according to Model-2Comp Performance results from thedifference between two training components In the case where 119896

2

is greater than 1198961 performance decreases first after the training

bout Afterwards the negative component decreases more quicklythan the positive component in the case where 119905

1is greater than 119905

2

resulting in performance recovery and peaking when the differencebetween the negative and positive components is the greatest Theresponse to a training bout is characterized by 119905

119899 the time necessary

to recover initial performance after the training session 119905119892 the time

necessary to reach maximal performance and 119901119892 the maximal gain

in performance for 1 training unit

the present study (Figure 1) The system operates in accor-dance with a transfer function resulting from the differencebetween two components one acting positively on perfor-mance ascribed to training adaptations and the second actingnegatively on performance ascribed to the fatiguing effects ofexercise Responses to training are thus characterized by theset of model parameters including two gain-terms 119896

1and 119896

2

and two time constants 1205911and 120591

2 The equation of Model-

2Comp is

119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1minus 1198962sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

2

(6)

To assess the statistical significance of Model-2Comp itsgoodness-of-fit was compared with that of a systems model


comprising only one training component (Model-1Comp)whose equation is

119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1 (7)

It was shown that the fitting of performance can be sig-nificantly improved with a model with 119896

2varying over time

in accordance with system input [3] We tested this modelnoted here as Model-3Comp whose equation is

119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1

minus

119899minus1

sum

119894=1

(119896 (0) minus Δ119896119894

2) sdot 119908119894sdot 119890minus(119899minus119894)120591

2

(8)

in which the value of 1198962at day 119894 is estimated by mathematical

recursion using a first-order filter with a gain term 1198963and a

time constant 1205913

Δ119896119894

2= 1198963sdot

119894

sum

119895=1

119908119895sdot 119890minus(119894minus119895)120591

3 (9)

We added the value of 1198962at time 0 in this study noted

1198962(0)

233 Estimation of Model Parameters and Statistics Theparameters for the models were determined by fitting themodel performances to actual performances for the entiregroup of rats using a mixed-effects model This model incor-porated a systematic component for the mean response ofthe population and a random component for each animalrsquosresponse around the mean The general model included (i)common time constants 120591

1for Model-1Comp 120591

1and 1205912for

Model-2Comp and 1205911 1205912 and 120591

3for Model-3Comp (ii) a

subject-specific intercept 119901(0) and (iii) subject-specific mul-tiplying factors for each component 119896


1

and 1198962for Model-2Comp and 119896

1 1198962(0) and 119896

3for Model-

3Comp The set of model parameters was calculated to pro-duce the equation that most closely fit the data points Usingthe generalized reduced gradient (GRG) algorithm in theExcel solver the parameters were determined by minimizingthe residual sum of squares (RSS) between the modeled andmeasured performances given by

RSS =119877

sum

119903=1

119873

sum

119899=1

(119901119899

119903minus 119901119899

119903)2

(10)

where 119903 is an integer corresponding to each rat (total number119877 being 11) and 119899 to each day during which performance wasmeasured (total number being 19 for each rat)119901119899

119903is the actual

performance and 119901119899119903is themodel performance at day 119899 for rat

119903Indicators of goodness-of-fit were estimated for each

model used in this study The Shapiro-Wilk test was used tocheck the normality of the distribution of both the trainingloads that is input of the model and the performances that

is input of the model The statistical significance of the fitwas tested by analysis of variance of the RSS in accordancewith the degrees of freedom (df) of eachmodel 12 forModel-1Comp 24 for Model-2Comp and 36 for Model-3CompTheadjusted coefficient of determination (Adj1198772) was computedto take into account the difference in df between the modelsThe mean square error on performance estimation (SE) wascomputed as RSS(119873minusdfminus1)The level of confidence for eachlevel ofmodel complexity was tested by analysis of variance ofthe related decrease in residual variationThe decrease in RSSexplained by the introduction of further model parameterswas tested using the 119865-ratio test in accordance with theincrease in df as described previously [15] Data in the textand Table 1 are expressed as means plusmn SD and the responses totraining are showed with SEM in Figures 2 and 3

234 Modeled Responses to Training With Model-2Compthe time response of performance to a single training boutwas characterized by 119905

119899 the time to recover performance and

119905119892 the time to peak performance after training completion

[16] computed as

119905119899=

12059111205912

1205911minus 1205912

ln(11989621198961

) 119905119892=

12059111205912

1205911minus 1205912

ln(1205911119896212059121198961

)

(11)

119901119892 the maximal gain in performance for 1 unit of training

was estimated as

119901119892= 1198961119890minus1199051198921205911minus 1198962119890minus1199051198921205912 (12)

To distinguish the short-term negative effect of thetraining doses from the long-term benefit the positive andnegative influences of training on performance (ip and inresp) were estimated as described previously [17] Theamount of training on day 119894 had an effect on performance onday 119899 quantified by

119864(119894

119899

) = 1198961119908119894119890minus(119899minus119894)120591

1minus 1198962119908119894119890minus(119899minus119894)120591

2 (13)

The values of in and ip on day 119899 were estimated from thesum of influences of each past training amount dependingon whether the result was negative or positive

in119899 =119899minus1

sum

119894=1

1003816100381610038161003816100381610038161003816

119864 (119894

119899

)

1003816100381610038161003816100381610038161003816

when 119864( 119894119899

) lt 0

ip119899 =119899minus1

sum

119894=1

1003816100381610038161003816100381610038161003816

119864 (119894

119899

)

1003816100381610038161003816100381610038161003816

when 119864( 119894119899

) gt 0

(14)

3 Results

Figure 2 shows the evolution in training work and per-formance Table 2 shows the statistics for the fitting ofperformance with the three tested models Although the fitwas statistically significant for allmodels onlyModel-2Compsignificantly improved the fit when compared with Model-1Comp (119875 lt 005) The third component in Model-3Comp


0

02

04

06

08

1

12

0 5 10 15 20 25 30

Perfo

rman

ce o

utpu

t (W

)

Time (days)

0

20

40

60

80

0 5 10 15 20 25 30

Trai

ning

inpu

t (J)

Time (days)

Figure 2 Quantification of training (systems input) and performance (systems output) Values are expressed in mean plusmn SEM Note that forthe training input the variability is very low because the animals had the same age and the same training load calculated as a percentage ofbody mass Thus SEM bars are hardly visible

Table 2 Statistics of model fitting

Model 1198772 Adj1198772 119865 ratio df 119875 SE

Model-1Comp 048 045 1497 12 196 lt0001 0209Model-2Comp 053lowast 047 878 24 184 lt0001 0202Model-3Comp 054 045 568 36 172 lt0001 0198Model-1Comp model using one first-order component Model-2Compmodel using two first-order components Model-3Comp model with twocomponents where the gain term for the negative component varies by usingone further first-order filter Adj1198772 adjusted coefficient of determinationdf degrees of freedom SE standard error Statistical difference compared toModel-1Comp lowast119875 lt 005

failed to give a description of performance variations com-pared with Model-1Comp and Model-2Comp (119875 gt 005) Itis noteworthy that the coefficient of determination adjustedto the model df was lower for Model-3Comp than for Model-2Comp

Because of its statistical significance the results fromModel-2Comp were retained for the analysis of the effects oftraining With the estimates of parameters of Model-2Comp(1205911= 531 days 120591

2= 43 days 119896

1= 00186 plusmn 00134 and

1198962= 00200plusmn 00157 sminus1) the response to a training bout was

characterized by 119905119899= 107 plusmn 146 days 119905

119899= 529 plusmn 204 days

and 119901119892= 00011 plusmn 00005W The variations in ip and in are

shown on Figure 3 ip which can be regarded as an index ofthe adaptations to physical training increased progressivelyall along the experiment whereas in the index of fatigueincreased during the first days of training each week before itplateaued with the daily sessionsThe 2 days without trainingbetween weeks allowed a complete recovery of past sessions

4 Discussion

In the present study Model-2Comp was retained as theoptimal model because statistically it provided the bestdescription of the effect of the response to resistance trainingin rats Contrary to the results in a previous report [3]Model-3Comp did not statistically improve the fit of the modelpossibly because of an insufficient amount of training work

000

020

040

060

080

0 5 10 15 20 25 30Time (days)

Influ

ence

of t

rain

ing

(W)

ipin

Figure 3 Mean plusmn SEM of the sum of positive and negativeinfluences of training on performance

This model is based on the assumption that the relation-ship between daily training work and performance has aninverted-U shape which implies that when the amount oftraining exceeds an optimal value of daily work performancewill decline because of the transient oversolicitation Theamounts of training in the present study may not have beengreat enough to allow the detection of such an effect Thevariations in fatigue elicited by the exercise over the entirestudy period were relatively small and Model-3Comp didnot increase the response to training compared to Model-2CompThis is supported by the estimates for the small valuesobtained for 119905

119899and 119905119892 which suggested that the rats coped

well with the trainingwork NeverthelessModel-3Comp is ofa great interest for exercise prescription because it allows formore detailed analysis of the detrimental effects of trainingwith heavysupraoptimal loads For this reason this prelim-inary study with an experimental animal model provides abasis for further research using Model-3Comp Indeed tooptimally capture the process of training it will be necessaryto increase the amount of training work and to use contrasted


training programs with periods of more intensified trainingfollowed by reduced training work Moreover this systematicmathematical procedure of modeling offers the possibility ofsimulating training effects in order to test different strategiesand it may thus be useful for advocating individualizedtraining programs which constitute the optimal adaptivestimulus This type of approach was developed to optimizethe training process in athletes [18 19] but with the animal asan experimental model it could be extended to those chronicdiseases for which exercise presents curative properties asalready employed in cardiac rehabilitation [20 21] It wouldthus be of interest to extend these strategies of rehabilitationprograms to rodent models suffering from other chronicdiseases (eg obobmice dbdbmice for type 2 diabetes andthe streptozotocinmodel for type 1 diabetes) as direct testingin patients would not be ethical

Another advantage of the animal model compared withhuman modeling of training effects is the high precision inthe quantification of training work and performance In thepresent study the training work was directly computed by themechanical work of the center of mass [22] Here the unitwas the joule whereas the training load for athletes isindirectly evaluated by the variation in heart rate as initiallyproposed by Banister or the number of repetitions in eachexercise bout [17 23 24]Themeasure of performance is alsomore accurate because it is computed from the power devel-oped according to the reference method of the center of mass[22] This measure in each training session also allows thecollection of a high number of performance values needed tofit the model

This study is the first to blend the mixed-effects model inthat proposed by Banister that is Model-2Comp Thisadvance in the technical sophistication of the modeling ledus to pool the data of the entire group of animals which offerstwo main advantages over the classical single-individualmodel The first advantage is that it provides great robustnessin the determination of the model parameters and insofarit increases the number of performance criteria withoutincreasing the degrees of freedom of the model in the sameproportion The second advantage is that it offers the pos-sibility of sacrificing several animals during training to gaininformation about the dynamics of the biological processesinvolved without appreciably degrading the precision of thetraining response quantification The only precaution thatneeds to be taken is to adapt the number of animals includedin the study according to the number of biological measuresplanned at different times so that the training response at theend of the training period is still representative with regard toa sufficient sample size

Last comparedwith studies on training effects in athletesthe animal model offers optimal conditions to link both thepositive andnegative effects of training to the transitory adap-tivemechanisms induced by the cell signaling pathwaysUntilnow the process of training adaptation was considered to belike a black box wherein performance output is the responseto training work With an animal model that conforms to thestandards for the ethical treatment of experimental animals itis possible to give the real physiological signification to thecomponents of the transfer function used to describe the

training effects on performance New hypotheses can thusbe formulated to explain the positive and negative trainingeffects on performance For example is the positive influence(ip) linked to the main protein synthesis-signaling pathwayunder the control of the mechanistic (or mammalian) targetof rapamycin MTOR or is it related to the signaling scaffoldthat is responsible for morphological adaptions (phenotypeATPase activity and hyperplasia) On the other hand canthe negative influence (in) be explained by exercise-inducedproteolysis a phenomenon which seems to be attenuated atleast in part by resistance training through attenuated induc-tion of atrogenes such as the muscle ring finger 1 (MuRF-1)[25]

5 Conclusion

Modeling the effects of resistance training is fully applicablein rodent and allows for the detailed analysis of the trainingadaptation process Model-2Comp was the most appropriatemodel to describe the training responses in the presentstudy The addition of contrasted periods to our trainingprogram may be promising for the application of Model-3Comp which would yield information on the optimalvalue of daily training work a major focus in research onindividualized training and rehabilitation programs Themixed-effects model offers two main advantages comparedwith individual classicalmodeling with (i) greater robustnessin the determination of the model parameters and (ii) thepossibility to determine the kinetic of the biological parame-ters by sacrificing several animals at critical times during thetraining programThe accuracy in quantifying training loadsand performance in the experimental condition of resistancetraining with rodents as well as the possibility of tightlycontrolling external factors makes it possible to upgrade thestructure of the training effects model and establish thebiological significance of the model components

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Thierry Busso and Robin Candau have equally contributed tothis work

Acknowledgments

The authors would like to thank Marie-Amelie Le Fur andFlorence Sabatier and Sara Laatar for her precious help intraining the animals and Catherine Carmeni for revising theEnglish paper

References

[1] E W Banister T W Calvert M V Savage and T Bach ldquoAsystems model of training for athletic performancerdquo AustralianJournal of Sports Medicine vol 7 pp 57ndash61 1975


[2] R Candau T Busso and J R Lacour ldquoEffects of training oniron status in cross-country skiersrdquo European Journal of AppliedPhysiology and Occupational Physiology vol 64 no 6 pp 497ndash502 1992

[3] T Busso ldquoVariable dose-response relationship between exercisetraining and performancerdquo Medicine and Science in Sports andExercise vol 35 no 7 pp 1188ndash1195 2003

[4] H de Jong and D Ropers ldquoStrategies for dealing with incom-plete information in the modeling of molecular interactionnetworksrdquo Briefings in Bioinformatics vol 7 no 4 pp 354ndash3632006

[5] S Girgis S M Pai I G Girgis and V K Batra ldquoPharmacody-namic parameter estimation population size versus number ofsamplesrdquoThe AAPS Journal vol 7 no 2 pp E461ndashE466 2005

[6] K Ogungbenro A Dokoumetzidis and L Aarons ldquoApplicationof optimal design methodologies in clinical pharmacologyexperimentsrdquo Pharmaceutical Statistics vol 8 no 3 pp 239ndash252 2009

[7] M Avalos P Hellard and J-C Chatard ldquoModeling thetraining-performance relationship using a mixed model in eliteswimmersrdquoMedicine and Science in Sports and Exercise vol 35no 5 pp 838ndash846 2003

[8] J Cholewa L Guimaraes-Ferreira T da Silva Teixeira et alldquoBasic models modeling resistance training an update forbasic scientists interested in study skeletal muscle hypertrophyrdquoJournal of Cellular Physiology vol 229 no 9 pp 1148ndash1156 2014

[9] N D Duncan D A Williams and G S Lynch ldquoAdaptationsin rat skeletal muscle following long-term resistance exercisetrainingrdquo European Journal of Applied Physiology and Occupa-tional Physiology vol 77 no 4 pp 372ndash378 1998

[10] G Begue A Douillard O Galbes et al ldquoEarly activation of ratskeletal muscle IL-6STAT1STAT3 dependent gene expressionin resistance exercise linked to hypertrophyrdquo PLoS ONE vol 8no 2 Article ID e57141 2013

[11] T AHornberger Jr andR P Farrar ldquoPhysiological hypertrophyof the FHL muscle following 8 weeks of progressive resistanceexercise in the ratrdquo Canadian Journal of Applied Physiology vol29 no 1 pp 16ndash31 2004

[12] S Lee E R Barton H L Sweeney and R P Farrar ldquoViralexpression of insulin-like growth factor-I enhances musclehypertrophy in resistance-trained ratsrdquo Journal of Applied Phys-iology vol 96 no 3 pp 1097ndash1104 2004

[13] J Borresen andM Ian Lambert ldquoThe quantification of trainingload the training response and the effect on performancerdquoSports Medicine vol 39 no 9 pp 779ndash795 2009

[14] T Busso and L Thomas ldquoUsing mathematical modeling intraining planningrdquo International Journal of Sports Physiologyand Performance vol 1 no 4 pp 400ndash405 2006

[15] H J Motulsky and L A Ransnas ldquoFitting curves to data usingnonlinear regression a practical and nonmathematical reviewrdquoThe FASEB Journal vol 1 no 5 pp 365ndash374 1987

[16] J R Fitz-Clarke R HMorton and EW Banister ldquoOptimizingathletic performance by influence curvesrdquo Journal of AppliedPhysiology vol 71 no 3 pp 1151ndash1158 1991

[17] T Busso R Candau and J-R Lacour ldquoFatigue and fitnessmod-elled from the effects of training on performancerdquo EuropeanJournal of Applied Physiology and Occupational Physiology vol69 no 1 pp 50ndash54 1994

[18] R HMorton ldquoModelling training and overtrainingrdquo Journal ofSports Sciences vol 15 no 3 pp 335ndash340 1997

[19] LThomas and T Busso ldquoA theoretical study of taper character-istics to optimize performancerdquoMedicine and Science in Sportsand Exercise vol 37 no 9 pp 1615ndash1621 2005

[20] S le Bris B Ledermann R Candau J M Davy P Messner-Pellenc and D le Gallais ldquoApplying a systemsmodel of trainingto a patient with coronary artery diseaserdquoMedicine and Sciencein Sports and Exercise vol 36 no 6 pp 942ndash948 2004

[21] S le Bris B Ledermann N Topin P Messner-Pellenc and Dle Gallais ldquoA systems model of training for patients in phase 2cardiac rehabilitationrdquo International Journal of Cardiology vol109 no 2 pp 257ndash263 2006

[22] W O Fenn ldquoWork against gravity and work due to velovitychanges in runningrdquo The American Journal of Physiology vol93 pp 433ndash462 1930

[23] T Busso K Hakkinen A Pakarinen et al ldquoA systems model oftraining responses and its relationship to hormonal responsesin elite weight-liftersrdquo European Journal of Applied Physiologyand Occupational Physiology vol 61 no 1-2 pp 48ndash54 1990

[24] A M J Sanchez O Galbes F Fabre-Guery et al ldquoModellingtraining response in elite female gymnasts and optimal strate-gies of overload training and taperrdquo Journal of Sports Sciencesvol 31 no 14 pp 1510ndash1519 2013

[25] H Mascher J Tannerstedt T Brink-Elfegoun B Ekblom TGustafsson and E Blomstrand ldquoRepeated resistance exercisetraining induces different changes in mRNA expression ofMAFbx and MuRF-1 in human skeletal musclerdquo The AmericanJournal of PhysiologymdashEndocrinology and Metabolism vol 294no 1 pp E43ndashE51 2008

Submit your manuscripts athttpwwwhindawicom

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Zoology


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process and ultimately to optimize the structure of themodel itself Rodent models authorize greater invasivenessyield more biological information and therefore providegreater insight into the adaptive processes that occur dur-ing training particularly regarding the link between theadaptive cell mechanisms and training effects In additionthe animal model could reduce the sources of variability inresponse to training compared with a human model Theinterindividual variability is naturally decreased in animalswith the same genetic background Obviously parametersexternal to training (nutrition sleep quality fatigue related toactivities other than training etc) are controlled in animalsas opposed to humans This homogeneity in the responses tophysical exercise in animals allows us to take advantage ofmixed-effects modeling to analyze the responses of a groupof animals taking interindividual variability into consider-ation When repeated measurements are made on severalrelated statistical units mixed-effects modeling allows amore robust estimation of model parameters than using onlyavailable individual data [4ndash6] The single-individual modelhas generally been used in human studies with the exceptionof onework inwhich themixed-effectsmodelwas applied to agroup of elite swimmers [7]

Among the training programs RE is particularly suitablefor animal studies because RE is associated with high gains inperformance muscle strength and muscle fiber cross-sectional area RE is characterized by exercise performedbetween 60 and 80 of the maximum load and severalexperimentalmodels have been developed to evaluatemuscleand physical performance in response to RE In rats vol-untary exercise based on ladder climbing activity has beenshown to induce muscle hypertrophy changes in muscletypology and increased force and power output [8] One ofthe first studies using ladder climbing as amodel of resistancetraining [9] showed that after 26 weeks of resistance trainingthe trained rats were able to climb 40 cmwhile carrying up to140of their bodymass without changes in the ratio betweenbody andmuscle (EDL and soleus) mass in comparison withcontrolsMore recently we found that rats could climb 1meterwhile carrying 150 of their body mass after 4 weeks ofresistance training in associationwith hypertrophy of 48 offiber IIx in FDP muscle [10] After 8 weeks the rats could liftup to 210 of their body mass Another study [11] demon-strated a 287 increase in the maximal amount of bodyweight that the animals could carry after 8 weeks of training(3 sessions a week)

REmodel offers the opportunity to quantify both trainingwork and performance in animal with a great accuracyThusthe twofold aim of the present study was to (i) test whetherthe systems models used to describe the training response inathletes could be applied in rats and (ii) verify the applica-bility of the mixed-effects model in animals with the samegenetic background in order to improve the statisticalstrength of the training response model

2 Methods

21 Animals and Experimental Design

211 Ethics Statement This study was approved by the Com-mittee on the Ethics of Animals Experiment of Languedoc

Table 1 Change in additional loads lifted by rats during the trainingprogram

Training sessions Load ( body mass) Mean load plusmn SD (g)1 to 5 50 1438 plusmn 1026 80 248 plusmn 2017 and 8 100 3126 plusmn 2469 to 13 120 3971 plusmn 34714 to 16 130 4509 plusmn 37817 and 18 140 4975 plusmn 41619 150 5397 plusmn 476

Roussillon in accordance with the guidelines from the FrenchNational Research Council for the Care and Use of Labora-tory Animals (permit number CEEA-LR-1069)

212 Animal Model Eight-week-old Wistar Han rats (277 plusmn15 g 119899 = 11) obtained from Charles River Laboratories(LrsquoArbresle Rhone France) were housed at a constant roomtemperature and humidity and maintained in a 12 12 h light-dark cycle They had access to standard rat chow (A04Scientific Animal Food amp Engineering Augy France) andwater ad libitum

213 Resistance Training Protocol The rats underwent 4weeks of progressive resistance training The exercise con-sisted of climbing a 1-meter-high homemade ladder inclinedat 85∘ ten times The ladder was adapted from the apparatusof Lee et al [12] Training sessions were held in the afternoonfive times aweekA cloth bag containingweightswas attachedto the base of the tail with tapeThree days before training therats were familiarized with the apparatus by climbing it twicewith 50 of body weight In accordance with the protocolproposed by Begue et al [10] the initial weight attached tothe tail was 50 of the rat body weight and was increasedprogressively until 150 after 4 weeks (Table 1) Each trainingsession consisted in one set of 10 repetitions with 2minrest between trials All rats were able to perform ten climbsper training session Rats from the same cage were trainedtogether Precisely rats were placed on a platform on the topof the ladder and one of them was put on the floor at the baseof the ladder The working rat quickly joined its congenersspontaneously

22 Training and Performance Quantification Training work(TW in J) was calculated as the potential work developedduring the training sessions

TW = (119898load + 119898rat) sdot 119892 sdot Δℎ sdot 119873 (1)

where mass (119898) is expressed in kg 119892 is the constant of thegravity on earth expressed in msdotsminus2 ℎ is the distance climbedin m and119873 is the number of repetitions

Performance was the power output developed during thefull climbing session computed as the work done against




(2)





119901 (119905) = 119901 (0) + 119908 (119905) lowast 119867 (119905 120579) (3)


119908 (119905) lowast 119867 (119905 120579) = int

119905

0

119908 (119904) sdot 119867 (119905 minus 119904 120579) 119889119904 (4)


119901 (119899Δ119905) = 119901 (0) +

119899minus1

sum

119894=1

119908 (119894Δ119905) sdot 119867 ((119899 minus 119894) Δ119905 120579) (5)



Time

Performance

0

0

Positivecomponent

Negativecomponent

k1

k2

tn tg

k1 minus k2

pg


2




2







1and 119896

2



2Comp is

119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1minus 1198962sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

2

(6)




119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1 (7)


2varying over time


119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1

minus

119899minus1

sum

119894=1

(119896 (0) minus Δ119896119894


2

(8)




Δ119896119894

2= 1198963sdot

119894

sum

119895=1

119908119895sdot 119890minus(119894minus119895)120591

3 (9)


1198962(0)



1and 1205912for





1


1 1198962(0) and 119896

3for Model-


RSS =119877

sum

119903=1

119873

sum

119899=1

(119901119899

119903minus 119901119899

119903)2

(10)


119903is the actual








[16] computed as

119905119899=

12059111205912

1205911minus 1205912

ln(11989621198961

) 119905119892=

12059111205912

1205911minus 1205912

ln(1205911119896212059121198961

)

(11)


was estimated as



119864(119894

119899

) = 1198961119908119894119890minus(119899minus119894)120591


2 (13)


in119899 =119899minus1

sum

119894=1

1003816100381610038161003816100381610038161003816

119864 (119894

119899

)

1003816100381610038161003816100381610038161003816

when 119864( 119894119899

) lt 0

ip119899 =119899minus1

sum

119894=1

1003816100381610038161003816100381610038161003816

119864 (119894

119899

)

1003816100381610038161003816100381610038161003816

when 119864( 119894119899

) gt 0

(14)

3 Results



0

02

04

06

08

1

12

0 5 10 15 20 25 30

Perfo

rman

ce o

utpu

t (W

)

Time (days)

0

20

40

60

80

0 5 10 15 20 25 30

Trai

ning

inpu

t (J)

Time (days)







2= 43 days 119896

1= 00186 plusmn 00134 and



119899= 529 plusmn 204 days



4 Discussion


000

020

040

060

080

0 5 10 15 20 25 30Time (days)

Influ

ence

of t

rain

ing

(W)

ipin











5 Conclusion






Acknowledgments


References


































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology




(2)





119901 (119905) = 119901 (0) + 119908 (119905) lowast 119867 (119905 120579) (3)


119908 (119905) lowast 119867 (119905 120579) = int

119905

0

119908 (119904) sdot 119867 (119905 minus 119904 120579) 119889119904 (4)


119901 (119899Δ119905) = 119901 (0) +

119899minus1

sum

119894=1

119908 (119894Δ119905) sdot 119867 ((119899 minus 119894) Δ119905 120579) (5)



Time

Performance

0

0

Positivecomponent

Negativecomponent

k1

k2

tn tg

k1 minus k2

pg


2




2







1and 119896

2



2Comp is

119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1minus 1198962sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

2

(6)




119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1 (7)


2varying over time


119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1

minus

119899minus1

sum

119894=1

(119896 (0) minus Δ119896119894


2

(8)




Δ119896119894

2= 1198963sdot

119894

sum

119895=1

119908119895sdot 119890minus(119894minus119895)120591

3 (9)


1198962(0)



1and 1205912for





1


1 1198962(0) and 119896

3for Model-


RSS =119877

sum

119903=1

119873

sum

119899=1

(119901119899

119903minus 119901119899

119903)2

(10)


119903is the actual








[16] computed as

119905119899=

12059111205912

1205911minus 1205912

ln(11989621198961

) 119905119892=

12059111205912

1205911minus 1205912

ln(1205911119896212059121198961

)

(11)


was estimated as



119864(119894

119899

) = 1198961119908119894119890minus(119899minus119894)120591


2 (13)


in119899 =119899minus1

sum

119894=1

1003816100381610038161003816100381610038161003816

119864 (119894

119899

)

1003816100381610038161003816100381610038161003816

when 119864( 119894119899

) lt 0

ip119899 =119899minus1

sum

119894=1

1003816100381610038161003816100381610038161003816

119864 (119894

119899

)

1003816100381610038161003816100381610038161003816

when 119864( 119894119899

) gt 0

(14)

3 Results



0

02

04

06

08

1

12

0 5 10 15 20 25 30

Perfo

rman

ce o

utpu

t (W

)

Time (days)

0

20

40

60

80

0 5 10 15 20 25 30

Trai

ning

inpu

t (J)

Time (days)







2= 43 days 119896

1= 00186 plusmn 00134 and



119899= 529 plusmn 204 days



4 Discussion


000

020

040

060

080

0 5 10 15 20 25 30Time (days)

Influ

ence

of t

rain

ing

(W)

ipin











5 Conclusion






Acknowledgments


References


































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology



119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1 (7)


2varying over time


119901119899= 119901 (0) + 119896

1sdot

119899minus1

sum

119894=1

119908119894sdot 119890minus(119899minus119894)120591

1

minus

119899minus1

sum

119894=1

(119896 (0) minus Δ119896119894


2

(8)




Δ119896119894

2= 1198963sdot

119894

sum

119895=1

119908119895sdot 119890minus(119894minus119895)120591

3 (9)


1198962(0)



1and 1205912for





1


1 1198962(0) and 119896

3for Model-


RSS =119877

sum

119903=1

119873

sum

119899=1

(119901119899

119903minus 119901119899

119903)2

(10)


119903is the actual








[16] computed as

119905119899=

12059111205912

1205911minus 1205912

ln(11989621198961

) 119905119892=

12059111205912

1205911minus 1205912

ln(1205911119896212059121198961

)

(11)


was estimated as



119864(119894

119899

) = 1198961119908119894119890minus(119899minus119894)120591


2 (13)


in119899 =119899minus1

sum

119894=1

1003816100381610038161003816100381610038161003816

119864 (119894

119899

)

1003816100381610038161003816100381610038161003816

when 119864( 119894119899

) lt 0

ip119899 =119899minus1

sum

119894=1

1003816100381610038161003816100381610038161003816

119864 (119894

119899

)

1003816100381610038161003816100381610038161003816

when 119864( 119894119899

) gt 0

(14)

3 Results



0

02

04

06

08

1

12

0 5 10 15 20 25 30

Perfo

rman

ce o

utpu

t (W

)

Time (days)

0

20

40

60

80

0 5 10 15 20 25 30

Trai

ning

inpu

t (J)

Time (days)







2= 43 days 119896

1= 00186 plusmn 00134 and



119899= 529 plusmn 204 days



4 Discussion


000

020

040

060

080

0 5 10 15 20 25 30Time (days)

Influ

ence

of t

rain

ing

(W)

ipin











5 Conclusion






Acknowledgments


References


































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0

02

04

06

08

1

12

0 5 10 15 20 25 30

Perfo

rman

ce o

utpu

t (W

)

Time (days)

0

20

40

60

80

0 5 10 15 20 25 30

Trai

ning

inpu

t (J)

Time (days)







2= 43 days 119896

1= 00186 plusmn 00134 and



119899= 529 plusmn 204 days



4 Discussion


000

020

040

060

080

0 5 10 15 20 25 30Time (days)

Influ

ence

of t

rain

ing

(W)

ipin











5 Conclusion






Acknowledgments


References


































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology







5 Conclusion






Acknowledgments


References


































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology








Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

Documents

Research Article Modeling the Responses to Resistance ... · Research Article Modeling the Responses to Resistance Training in an Animal Experiment Study AntonyG.Philippe, 1 GuillaumePy,