Journal of Strength and Conditioning Research, 2006, 20(11, 36-42© 2006 National Strength &. Conditioning Association

PROGRAM DESIGN BASED ON A MATHEMATICALMODEL USING RATING OF PERCEIVED EXERTION FORAN ELITE JAPANESE SPRINTER: A CASE STUDY

SHOZO SUZUKI,' TASUKU SATO, AKINOBU MAEDA,^ AND YASUO TAKAHASHI^

'Human Performance Laboratories, Faculty of Physical Education, Sendai College, Miyagi, Japan; -Faculty ofHuman Informatics, Tohoku-Gakuin University, Miyagi, Japan.

ABSTRACT. Suzuki S., T. Sato, A. Maeda, and Y. Takahashi.Program design based on a mathematical model using Rating ofPerceived Exertion for an elite Japanese sprinter: A case study.J. Strength Comi. Has. 20(l>:36^2. 2006.—We investigated theeffects of program design on 400-m sprint time by applying aRating of Perceived Exertion (RPE) mathematical model totraining performance. The subject was 24 years old and hadheen training for 9 years. His hest performance in 400-m sprintcompetitions was 45.50 seconds. Body weight, resting heart rate,training time and RPE wore monitored daily after training ses-sions. Similarly, performance in 400-m races was recorded 9times during 2003. At the World Championships in Athletics inFrance, the subject's team placed eighth in the 1,600-m relay.The RPE mathematical model was ahle to predict changes inperformance. Rate of matching was statistically significant (r =0.83, F ratio = 34.27, p < 0.0011. Application ofthe RPE math-ematical model to tbe design of a training program specific tothe needs of a 400-m sprinter indicates a potentially powerfultool that can he applied to accurately assess the effects of train-ing on athletic performance.

KKY WORDS, monitoring, performance, conditioning, monotony

INTRODUCTION

he uitimate goal of training is to prepare ath-letes to perform at their hest at important com-petitions. To achieve this goal, athletes musttrain to improve their competitiveness over a

period of 1 or several years. Designing a suitahly strin-gent training program requires an appreciation of theneed for implementing, analyzing, assessing, and modi-fying training regimens hased on the specific require-ments ofthe sport under consideration. The potential tosubsequently assess the effectiveness of these differentcomponents would he particularly helpful.

Calvert et al. (12) investigated relationships betweentraining and performance using a mathematical modelthat manages training as input data, and changes inphysical performance due to training as output data.Here, input impulses were training stimuli, and impulseresponses were changes in physical performance due totraining. By incorporating these 2 antagonistic functions;namely, the negatives of training (fatigue) and the posi-tives of training (fitness! into impulse responses, changesin physical performance were determined as the sum oftraining inputs and impulse responses. Using this model,the relationship between training and physical perfor-mance bas been clarified in sports including long-distancerunning (5), triathlon (4), swimming (3, 22), cycling (7, 9),running (23, 27), hammer throw (8), weightlifting (10,11), and rowing (30). A strong, positive correlation has

heen documented hetween actual and predicted values ofphysical performance. In addition, the time constant hasheen reported at 38-60 days for positives and 2-13 daysfor negatives, suggesting tbat tbe rate of negative cbangeis faster than the rate of positive change. Fitz-Clarke etal. (14) conducted a simulation study using a model tocalculate the duration of training required to maximizephysical performance. In tbis manner, by calculating co-efficients tbat could improve or worsen training effectshased on a given model, tbe effectiveness of tapering inmaximizing physical performance bas been scientificallyverified.

A device that monitors changes in heart rate (HR)during training must be worn in order to apply tbe train-ing impulse (TRIMP) matbematical model, developed byBannister et al. and described in previous studies (3-5,23), to routine sports training. Without using this devicein combination with an HR monitor to determine totalamount of daily training, the TRIMP matbematical modelcannot be easily applied. We therefore previously inves-tigated wbetber the TRIMP mathematical model, wbicbis capable of predicting performance, could be applied toJapanese suhjects (28).

Borg et al. (6) reported tbat the Category Ratio Scale(CR-10) is responsive to changes in HR and blood tactatelevel. To utilize tbis scale at training sites in a convenientmanner, TRIMP, which is calculated as the product ofthecoefficient of blood lactate level, exercise %HR,,,,,.,, andtraining time, was replaced with tbe rating of perceivedexertion (RPE) (16), a modification ofthe CR-10 scale de-veloped by Horg et al. to calculate training volume ac-cording to tbe following formula: training load = (trainingtime X session RPE). A study comparing performancepredictions displayed strong positive correlations betweentbe 2 models (27).

Tbe present study investigated whether tbe RPEmatbematical model, wbicb is easily applied to routinetraining, is useful in preparing, implementing, analyzing,and assessing a yearlong training program for a top 400-m sprinter. We also wanted to determine whether tbemodel was capable of evaluating athlete condition basedon conventional pbysiological parameters.

METHODS

Experimental Approach to the ProhlemTraining volume, fatigue, recovery, and performancewere assessed daily in an elite Japanese 400-m sprinterto monitor cbanges in tbese parameters over a period of1 year. Furtbermore, a case study was conducted to as-

DESK",N ON A M A T H F M A T I C A I . MtlDEL 3 7

Months

Peak

Schedule

Macro

Technique

Physical

JAN ; FEE

u1 1 1

MAK APK MAY : .HINE i JULY

1 y L ' U 1 iAUG iSEPTi OCT 1 HOV

djii 1CKC

1 11 2 a 4 E •: 7 -. 9

1- ChBini.-Ji.pBn Inici.! Tisili CanpetiUcti T Fukushima Champiornhipa3ThtjhofcuSludBntC«npstititjn 8' 9th Wstlii ChsmpionEhip iti ALhlatBii Mjto InUtnati'MiJC^mpstiUon ff Habanal Chsmpionships4 Th^hsku intetc^llaguUChanipiaiKhips S Kalisnal UiiinUuning';Bmps l' -S

Preparation

3 4 5

C DID petition

6 7 fl 9 1 lo: 11 \ 12! ! 1

13

Arm dri-v/RvJJtrrt Aonad/FiTn/[>riva

R

1 2

FIGURE 1. Program design in 2003.

certain wbetber a performance-peaking program de-signed hased on an RPE mathematical model would heeffective in actual competition. Tbe training program de-signed in 2003 for tbe subject by his coach comprised sev-eral macrocycles (rests, preparations, and competitions)and 13 mesocycles (Figure 1). In 2003, tbe subject com-peted in the following competitions: China-Japan IndoorTrack Competition {Fehruary 22). Toboku Student Com-petition (April 12), Mito International Competition (May5), Toboku Intercollegiate Cbampionships (May 18), Jap-anese Track and Field Cbampionsbips (June 8), JapaneseIntercollegiate Cbampionships (July 4), FukusbimaCbampionships (July 13), Ninth World Championships inAthletics (August 23-31), and National Cbampionsbips(October 28). For a period of almost 1 year, from January7 to December 20, 2003, the suhject was instructed tokeep a training journal recording morning HR, bodyweight, RPE, category ratio pain scale (CPS), and totalquality recovery (TQR). Whether tbe RPE matbematicalmodel could predict actual performance was ascertainedin four competitions up to May 2003. Because the modelwas shown to he able to predict performance, a perfor-mance-peaking training program was designed using tbemodel in an attempt to yield optimal performance duringsubsequent important competitions.

All data were analyzed using Excel software (ExcelSoftware, Placitas, NM) and were available to the sportsscientist, coacb, strengtb-and-conditioning specialist, andathlete so tbat they could visually ohserve daily changesin the ahove-mentioned parameters.

SubjectThe suhject was a 24-year-old track athlete (height, 174.5cm; weight, 63 kg) witb a 9-year background in trainingwbo won the 400-m sprint in tbe Japanese Track andField Championship in 2003 and 2004, was in tbe teamthat finisbed eighth in tbe 1,600-m relay at the NinthWorld Cbampionsbips in Atbletics in 2003, and was se-lected to represent Japan in the 2004 Athens Olympics.Informed consent was obtained after thorough explana-tion ofthe study objectives and methods. Study protocolswere approved by the Ethics Review Board of Sendai Col-lege, Japan.

Parameters MeasuredTbe subject measured HR hy palpation ofthe radial pulsefor 1 minute while still in bed in the morning, then im-

Rating

012345678g10

Descriptor

RestVery EasyEasyModerateSomewhat HardHard

Very Hard

Very, Very HardMaximal

FKJURE 2. Tbe subject's rating nf perceived exertion I RPE)was obtained with the use of a modified Borg scale (16). Thesuhject was shown the scale approximately 30 minutes follow-ing the conclusion of the training hout and asked "How wasour training today?"

mediately weighed bimself to an accuracy of 50 g usingUC-300 scales (Measurement Specialists, Huntsville, AL).

To assess the effects of training on tbe body, the sub-ject was asked RPE following tbe completion of eachtraining session using tbe session RPE scale developedby Foster and Lebmann (16; Figure 2). Subjective musclepain was assessed using the CPS scale developed by Ar-vidsson et al. (2; Figure 3). To assess RPE and CPS dur-ing exercise sessions, standard instruction and anchoringprocedures were explained during a familiarization ses-sion (25). At 30 minutes after the end of eacb trainingsession, the subject was asked, "How was your trainingtoday?" to determine RPE score, and "How are your mus-cles?" to determine CPS. Tbe suhject tben stated scoresfor all activities during tbe training session. Similarly, todetermine recovery from the training ofthe previous day,subjective recovery was assessed every morning using tbeTQR scale developed hy Kentta and Hassmen (21; Figure4) and the CPS scale.

The TQR scale was used in the same manner as theRPE and CPS scales. The subject was shown tbe scalebefore breakfast and was asked "How is your conditionnow?" to determine his TQR score.

Table 1 sbows tbe contents of microcycle training andassessment of tbe training progi'am in terms of load, mo-notony, and strain, whicb were quantified according totbe metbods reported by Foster and Lehmann (15, 16).

The subject was required to record in bis trainingjournal tbe duration of training and RPE las subjectiveexertion) 30 minutes after the end of daily training.Training load was calculated by multiplying duration oftraining by RPE. For example, the suhject performed rep-etition training on Tuesdays, so tbe load for Tuesdays was180 X 6 = 1,080 units. Mean (± SD} weekly load wascalculated as 686 ± 661 units.

Monotony was calculated by dividing the weekly av-erage by the standard deviation (1.04). In other words,training monotony resulted in a small standard deviationand a high monotony value. A small monotony value in-dicated a high degree of training variation.

Strain was calculated by multiplying the mean weeklyload hy monotony (4,994). In otber words, training with

38 SUZUKI, SATO, MAEDA ET AL.

Rating

20 =151

12110-9 -8 -7 -6 -5 ~4 —

3 -

Q

1.0-

0.5-

oJ

Descriptor

Extremely strong

Very strong

Strong

Moderate

Light

Very light

Extremely light

—No pain

FKiUKK 3. Subjective muscle pain was assessed using thecategory ratio pain scale (CPS) developed by Arvidsson 12). At30 minutes after the end of each training session and heforebreakfast, the subject was asked "How are your muscles?" todetermine the CPS score.

a high degree of" variation resulted in a low monotonyvalue and thus low strain.

Even if total weekly load was low, repeated trainingmonotony (long, low-intensity training! performed on adaily basis would increase the level of monotony andstrain and could result in overtraining and sports injury

Rating

6789

1011121314151617181920

Descriptor

Very, Very Poor Recovery

Very Poor Recovery

Poor Recovery

Reasonable Recovery

Good Recovery

Very Good Recovery

Very, Very Good Recovery

FIGURE 4. Subjective recovery was assessed using Kenttaand Hassmen's total quality recovery scale 121), The subjectwas shown the scale hefore hreakfa.st and was asked, "How isyour condition now?"

(1, 15). If long, low-intensity training was performed theday after short, high-intensity training to reduce fatigue,training load would be consistently comparable, increas-ing monotony. If this type of training monotony continuedfor periods of weeks, months, and years, the degree ofphysical stress would increase, diminishing training ef-fects and increasing the risk of overtraining (19).

Mathematical Model Using Rating of PerceivedExertion

Recorded training parameters were used for a systemmodel adapted from the model developed hy Morton et al.(23). Levels of fitness and fatigue, p(t) and f(t), were ob-tained by convolving training load (w(t) ^ training timeX session RPE), with training responses g(t) and h(t), asdescribed by Banister and Hamilton (5). The value w(t)is expressed in arbitrary units; so that:

pit) = w(t)-g(t), and

fit) - wi.t)-h(t).(1)(2)

TABLE 1. Evaluation of the load, monotony, and strain associated with a training program.

Day Training sessionDuration

(min) Load

MondayTuesdayWednesdayThursdayFridaySaturdaySundayMean weekly load

RestHigh-tempo trainingShort interval. Resistance trainingRestUp-and-down hill trainingJump trainingJog 5 km, easy

Standard deviation of mean weekly loadMonotony (mean weeklyTotal weekly load (meanStrain (total weekly load

load/standard deviation of mean weekly load)weekly load x 7)X monotony)

0180120

018018030

0660974

01080720

016201260

120

686661

1.0448024994

* RPE = rating of perceived exertion.

Pi«x~,KAM DFSICN BASFD ON A MATKFMATICAL MOD[-:I_ 39

300 r RPE -a-CPSl 1 Competitions 20

1(12 aiK •.il]3 *12 6112 7/12 8IIZ 9/12 10/12 11/12 12/12

D a t e

FICURE 5. Weekly changes in training time, rating of per-ceived exertion (RPE), and category ratio pain scale (CPS).

In the description by Banister and Hamilton (5), themathematical form of the functions g(t) and hit) were asfollows:

git) = e "'•'., and

h(t) - e " ^

(3)

(4)

where T, and T, represent decay time constants for fitnessand fatigue (first estimated as 45 days and 15 days, re-spectively, then refined by iteration), and t is time.

An index of performance was obtained from differencehetween levels of fitness and fatigue weighted by a coef-ficient k:

ail) = k,-p(t^ - 2-/f ) 'fj)where fe, and k.^ represent the proportionality factors offitness and fatigue (first estimated as /;, = 1 and k.^ = 2,then refined by iteration).

In our apphcation, the mathematical form of responsefunctions were as follows:

gU) =

hit) =

and (6)

(7)

Performance ait) was determined as the difference be-tween fatigue and fitness levels, as such:

ait) - pit) - fit) (8)

By recurrence, p(t), f(t), and thus a(t) could be calculatedusing previous successive training loads and individualparameters T,, T , ^i, and k.^.

Model parameters were determined by fitting modelperformances to the 400-m races during the 9 competitionperiods. These parameters were obtained by minimizingthe residual sum of squares (RSS) hetween modeled andactual performances. A multiple linear regression methodwas used after decay time constants were fixed.

Statistical AnalysesIndicators of goodness-of-fit were estimated for the levelsof model. Coefficients of determination ir') hetween mod-eled and actual performances were calculated. Statisticalsignificance of fit was tested using analysis of varianceon the RSS. The statistical F test was used to estimatelevel of significance for model fit.

RESULTSTraining Time and Subjective ParametersFigure 5 shows weekly changes in training time, RPE 30minutes after training, and CPS for 2003. Training time,

inv, 2/lK 3/12 A/\2 6112 6/12 7/12 B/12 9/lE 10/lZ l l / l f . 12/12

D a t e

FIGURE 6. Weekly changes in morning category ratio painscale (CPS) and total quality recovery (TQRl including thepeaking periods.

•W.>Bht-»-R.=t-HR [ I Competitions

I . M U 11 i I

ANiu i

1/12 2IIZ HII7. 4/12 fiil2 6/12 H/IH 9(12 I(V12 11/12 !2/IK

D a t e

FIGURE 7. Weekly changes in morning pulse rate and weight.

RPE, and CPS decreased hefore the Japanese and WorldChampionships in 2003. Mean annual RPE and CPS werehigh at 5.6 and 6.6, respectively, indicating that the sub-ject underwent physically demanding training during thetraining season. In addition, during these 2 major cham-pionships, CPS was 0 (no pain) and TQR was 17 to 20(favorable recovery), indicating that the subject competedin the 2 major championships after having sufficientlyrecovered from muscle pain and fatigue (Figure 6).

Morning Heart Rate and Body WeightFigure 7 shows weekly changes in morning HR and bodyweigbt, which decreased as the subject prepared for the2 major championships. Morning HR and body weight onthe day of the 2 major championships were 58 b-min 'and 61.8 kg, respectively. In 2003, the degree of daily fiuc-tuation in morning HR and body weight in 2003 was 10b-min ' and 3.1 kg, respectively.

Load, Monotony, and StrainFigure 8 shows weekly changes in load, monotony, andstrain in 2003. As an indicator of total amount of training,load decreased as the subject prepared for the 2 majorchampionships. Monotony, indicating training variation,decreased from 1.02 to 0.8 hefore the national champi-onships and from 1.4 to 0.8 before tbe world champion-ships. Furthermore, strain also decreased before both ma-jor championships.

Mean monotony was 0.74 ± 0.4, suggesting that the

40 SUZUKI, SATO, MAEDA ET AL.

15000 r

10000

5000

1112 Sn2 3112 Alls SI12 ll\2 8fia 9(12 ions 11112 1211?.

oBo

s

[•-"\-AAAA ;

1(18 2(12 3(12 4(ia 5(12 «1S 7(12 WIK 9(12 10(12 11(12 12(18

20000

16000

I 12000

W 8000

40O0

01(12 2(12 3(12 4(12 5(12 «12 7(12 8112 9(12 10(12 11(12 12(12

D a t e

FicuRE 8. Weekly changes in load monotony and strain.

subject underwent training with a high degree of varia-tion.

Actual and Predicted PerformanceFigure 9 shows the relationship between actual perfor-mance and the performance curve derived using the RPEmodel and times for 400-m sprints in the 9 competitions.The mathematical model was prepared using the follow-ing coefficients and time constants for fatigue and fitnessin the subject:

FitU) = l-w(t}-e "^\ and

Failt) = 2-w(t)-e "^''.

These coefficients were calculated to achieve minimalRSS between actual and predicted values. While predict-ed value was lower than the actual value for the firstindoor competition, actual and predicted values were sim-ilar for outdoor competitions (r- = 0.83; F ratio = 34.27,p < 0.0011.

DISCUSSION

The 2003 training plan for the subject, comprising severalmacrocycles containing rests, preparations, competitions,and 13 distinct mesocycles, was designed to ensure thatthe condition of the subject would peak at the major

^ 80000FaUgue

1(13 3(ia 3(13 1(13 5(13 «(13 1112 BII3 9(13 10(13 11

§ 30000g -

3

- II ! T(13 8(13 9tl3 1(U13 11(13

Date

44

46

48 J

FiGURK 9. Changes in actual and predicted performance.

championships. According to introspective reports on per-formance, the subject wrote that he could win the 400-msprint at the Japanese championships, his most impor-tant competition in 2003, and achieved this in a time of45.63 seconds. In the preliminary race, his time was 0.13seconds faster than in the final race, and satisfied the Astandard (45.55 seconds) for the World Championships inAthletics. Based on results from the Japanese champi-onships, his coach redesigned the training program toprepare him for the Ninth World Championships in Ath-letics in August. With a time of 46.53 seconds, approxi-mately 1 second slower than his personal best, the suhjectfailed to make the 400-m final in the world champion-ships. However, in the 1,600-m relay, he ran anchor legand finished eighth with a time of 3 minutes 2.35 seconds.

Thayer (31) found that stimulation, overloading, ad-aptation, and training effects correlated with fast recov-ery, stating that alternating periods of training and restare important to maximize cyclic training. This is partic-ularly important when designing a yearlong trainingplan. Thayer also stated that a yearlong training programwith a high degree of variation can maintain a low mo-notony level. Regarding the yearlong training programdesigned for the present subject, a 5-mesocycle block wasscheduled before each important competition. In otherwords, the program specified the amount of training(load) to be tapered before each important competition.As to changes in monotony and strain, these parameterswere low before the national and world championships,enabling the subject to enter while undergoing trainingwith a high degree of variation, to reduce the amount ofphysical stress. Foster and Lehman (15, 16) followed theload, monotony, and strain of elite long-distance runnersfor 2 years and reported that training with a high degreeof variation and low level of monotony improved compet-itive performance. As a result, they designed the secondyear of the training program to minimize training mo-notony. In our previous research on competitive rowers,

DI;SIC;N ON A MAIHrMATICAL MODFl. 41

level of monotony was >3 before a competition, and per-formance was not observed to peak at tbe competition (26,29). Mean monotony for tbe present subject was muchlower, at 0.74, indicating tbat tbe yearlong training pro-gram incorporated a bigb degree of variation.

Morning HR, serving as an objective physiological pa-rameter, decreased before tbe 2 major cbampionsbips. Ontbe day of tbe cbampionsbips, morning HR was 58b-min ', lower tban tbe mean morning HR of 60 b min '.Dressendorfer et al. (13) reported tbat wben fatiguesymptoms worsened, morning HR increased by more tban10 b min '. Wbile morning HR did not increase by moretban 10 b-min ' for our subject before any of tbe impor-tant competitions, subjective and objective parameters ofmonotony, strain, TQR, and CPS were poor at times wbenmorning HR did increase by >10 b-min '. Tbese findingssuggest tbat wben planning and assessing yearlong train-ing programs, monitoring basic pbysical parameters isimportant for determining pbysicai conditioning of atb-letes.

Fry et al. (17, 18) reported tbat tbe major objectivesof periodization, wbicb is at the core of training programdesign, are to prevent overtraining and to ensure peak ormaximized performance at appropriate times. Further-more, tbe key for successful program design is to ensurerecovery from fatigue (18, 22).

Loren et al. (20) suggested tbat training effects willbe maximized wben tbe fitness-fatigue model is effective-ly utilized witbin any yearlong program design.

In the present study, the RPE model, wbicb reflectedtbe aftereffects of fatigue and fitness, was used to predictperformance in 400-m sprints, and predicted and actualperformances were compared in 4 competitions up toMay. The results showed that the model could predictperformance ir^ = 0.88; F ratio = 52.04; p < 0.001}. Fur-thermore, the sports scientist, coach, and strength-and-conditioning specialist each comprehensively examinedthe performance curve derived from tbe matbematicalmodel and cbanges in various parameters, sucb as morn-ing HR, CPS, TQR, and monotony, and concluded tbat tbeRPE mathematical model could be utilized as a tool foraiding tbe design of training progi'ams. Next, the sportsscientist performed a simulation study using the RPEmathematical model to maximize subject performanceduring tbe Japanese Track and Field Cbampionships byaltering training volume, and tben tbe idea of preparinga microcycle peaking program was provided as feedbackto tbe field. Based on tbese data, tbe coacb prepared thefinal program. During training, the sports scientist andstrength-and-conditioning specialist analyzed and as-sessed changes in various parameters and reported tberesults back to tbe coacb. Based on tbis feedback, tbecoacb readjusted tbe training volume. Subsequently, atthe Japanese Track and Field Championships, the suhjectwas able to run bis personal best at 45.50 seconds. TbeRPE mathematical model was used again to prepare fortbe Nintb World Cbampionsbips in Athletics. However,because training volume was adjusted by tbe bead coachof the national team during tbe 3-week overseas camp,tbe present system could not be effectively implementedin the subject. Using data collected during tbe camp, theRPE mathematical model showed tbat tbe subject en-tered the World Championships during a low point of hisperformance curve.

Tbe present findings suggest tbat yearlong programs

designed utilizing tbe RPE matbematical model can sim-ulate performance fluctuations in terms of intensity, du-ration, and frequency. Overtraining can tbus be prevent-ed and periodization used to maximize performance at aparticular competition. Furtbermore, maximization ofperformance at a particular competition requires not onlyutilization of tbe RPE mathematical model, but also tbecombination of objective and subjective parameters sucbas morning HR, CPS, TQR, and monotony. Program de-sign accounting for these parameters sbould prove usefulin routine training for top atbletes.

For a program such as the described model to functionoptimally, tbe sport scientist, sport coach, and strengtb-and-conditioning professional must plan the program to-gether and share goals and strategies.

PRACTICAL APPLICATIONS

In practical terms, program design involves manipulatingtraining intensity and volume wbile being respectful ofthe seasonal demands of the specific sport and athlete.Many coaches prepare training programs to peak atbleticperformance during important competitions. To maximizeperformance during important competitions, the qualityof training programs must be improved. An RPE mathe-matical model was used as a tool for designing trainingprograms, and combined witb sucb subjective and objec-tive parameters sucb as CPS, TQH, and monotony, tbemodel was sbown to function as an effective tool in tbefield.

This system comprising a mathematical model andpbysical condition assessments runs on Excel, and dailychanges in performance can be visually cbecked in theform of figures and charts. In addition, maximal perfor-mance during important competitions can be simulatedby adjusting training time, intensity, and frequency. Thepresent results show that by adding performance predic-tions based on a matbematical model to tbe existing pe-riodization metbod, optimal performance can be targetedduring important competitions while preventing over-training. In addition, by collecting more data, tbe presentsystem sbould contribute to improving tbe quality oftraining programs designed by coaches.

REFERENCES

1. ANI)KI{.S()N, L., T. TRTPLETT-MrBmnE, C. FOSTER, S. DOGER-STEIN, AND G. BKK'E. Impact of training patterns on incidenceof illness and injury during a women's c-ollegiate basketballseason. J, Strength Cond. Res. 17:734-738. 2003.

2. AjiViiissoN, I. Rehabilitation of athlete's knee. Med. Sport Sci.26:238-246. 1987.

3. BANISTER, E.W.. AND T.W. CALVEKT. Planning for future per-formance: Implication for long term training. Can. J. Appl.Sport Sci. 5131:170-176. 1980.

4. BANISTKK, E>.W., J . B . CARTF.K, AND P.C. ZAEKADSA. Trainingtheory and taper: Validation in triathlon athletes. Eur. J. Appl,Physiol. 79:182-191. 1985.

5. BANISTKR, E.W., AND C.L. HAMILTON. Variations in iron statuswith fatigue modeled from training in female distance runners.Ear. J Appl. Physiot. 54:16-23. 1985.

fi. BoRU, G.A.. P. Pi.AsswK.Mi., AND M. LANCERSTROM. Perceivedexertion related to heart rate and blood lactate during arm andleg exercise. Eur. J. Appl, Physiol. 65:679-685. 1987.

7. Biisso. T., H. BENOIT, R. BONNEFOY, \., FKASSON, AND J.R. LA-COUR. El!'[>cts of training frequency on the dynamics of perfor-mance response to a single training bout. -J. Appl. Physiol. 92:572-580. 2002.

42 SUZUKI, SATO, MAEDA ET AL.

8. BL-SKO, T., R. CANDAU. AND J.R. LACOUH. Fatigue and fitnessmodelled from the effects of training on performance. Eur. J.Appl. Physiol. 69:50-54. 1994.

9. Birss(J, T., C. CARASSO, AND J.R. LACOUK. Adequacy of a sys-tems structure in the modeling of training effects on perfor-mances. J. Appl. Physiol. 7:2044-2049. 1991.

10. Bussd, T., K. HAKKINEN, A. PAKARTNEN, C. CAHASSO, J.R. LA-COUK, P.V. KOMI, AND H. KAUHANKK, A systems model of train-ing responses and its relationship to hormonal in elite weight-lifters. Eur. J. Appl. Physiol. 61:48-54. 1990,

11. Busso, T., K. HAKKINEN, A. PAKARiNi':N, H. KAUHANEN, P.V.KOMI, AND J.R. LACOUR. Hormonal adaptations and modeledresponses in elite weight-lifLers during 6 weeks of training.Eur J. Appl. Phy.^iol. 64:381-386. 1992.

12. CALVERT, T.W., E.W. BANISTER, M.V. SAVAGE, AND T. BACH. Asystems mode! of the effects of training on physical perfor-mance. IEEE Tranfiadionti on Svslerii.s, Man. and Cybernetics.6:94-102, 1976.

13. DKE-SSENHOREEK, R.H., C.E, WAIIA, AND J . H . SCAEE, JR. In-creased morning heart rate in runners: A valid sign of over-training? P/i.y,s. Sportsmed. I3(8):77-86. 1985.

14. FITZ-CLAKKE, J.R., R.H. MORTON, AND E.W. BANISTER. Opti-mizing athletic performance hy influence curves, J. Appl. Phy-siol. 71(31:1151-1158, 1991.

15. FOSTER, C. Monitoring training in athletes with reference toovertraining syndrome. Med. Sci. Sports Exerc. 30:1164-1168.1997.

16. Fos-!'ER, C. AND M. LEHMAN. Overtraining syndrome. In: Run-ning Injuries, G.N. Guten, ed. Philadelphia: W.B. Saunders.1996. pp. 173-188.

17. FRY, R.W., A,R. MORTON, AND D. KEAST. Periodisation of train-ing stress—A review. Can. J. Sport Sci. 17(3):234-240. 1992.

18. FRY, R.W., A,R. MORTON, AND D. KEAST. Periodisation and theprevention of overtraining. Can. J. Sport Sci. 17(3):241-248.1992.

19. LEHMAN, M., C. FOSTER, AND J, KEUL. Overtraining in endur-ance athletes: A hrief review. Med. Sci. Sports Exerc. 25:854-862. 1993.

20. LOKEN, Z.F.C., AND L,B, JACQE. The fitness-fatigue model re-visited implications for planning short- and long-term training,J. Strength Cond. Res. 25(6):42-51. 2003.

21. KJ-;N'ITA, G., AND P. HASSME.N. Overtraining and recovery.Sports Med. 26{1):9-16. 1998.

22. MORTON, R.H. Modelling training and overtraining. J. SportsSci. 15:335-340, 1996.

23. MORTON, R.H., J,R, FITZ-CLARKE, AND E.W. BANISTER. Mod-eling human performance in running. J. Appl. Physiol. 69:1171-1177. 1990.

24. MujiKA, L, T. Bosso, L. LACOSTE, F . BARALK, A. GEYSSANT,AND J.C. CHATARF), Modeled responses to training and taper incompetitive swimmers. Med. Sci. Sports EUTC. 28(2) :251-258.1996,

25. NOBLE, B,J. , ANH K.J. RORERTSON. Perceived Extortion. Cham-paign, IL: Human Kinetics, 1996.

26. SUZUKI, K., A. MAEDA, AND Y. TAKAHASHI. Attempt of monot-ony analysis to a result of the boat race as.sociated with thetraining program for the Japanese rower. J. Hum. Info. 9:39-48. 2003,

27. Si.-zuKi, S,, T. SATO, AND Y. TAKAHASHI. A typical example ofmodeling human performance in 5000 m running time. Can. J.Appl. Physiol. 27lSuppl.):47-48, 2002.

28. SUZUKI, S., T. SATO, AND Y. TAKAHASHL The effects of totaltraining volume on 5,000 m running time. Hiro Kyuyo. 18(1):31-42. 2002,

29. SUZUKI, S., T, SATO, AND Y. TAKAHASHI. Diagnosis of trainingprogram for a Japanese rower by using the index of monotony.Can. ,). Appl Physiol. 28lSuppl.1:105-106. 2003,

30. SUZUKI, S., T. SATO, AND Y, TAKAHAKHI. Estimation of a train-ing program for one Japanese rower hy using tbe index of mo-notony and the mathematical model. Hiro Kyuyo. 19(l):75-84.2003.

31. THAYER, R. A systematic approach to training an athlete.Coaching Rev. 17:29-33. 1980.

Address correspondence to Shozo Suzuki, sz-suzuki@scn,ac.jp.