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Table of Contents
Year : 2019  |  Volume : 62  |  Issue : 6  |  Page : 241-244

Identification of the force–velocity curve on dynamic resistance exercise for rats

1 Research in Exercise and Nutrition in Health and Sports Performance-PENSARE, Graduate Program in Movement Sciences, Federal University of Mato Grosso do Sul, Campo Grande, Brazil
2 Graduate Program in Health and Development in the Midwest Region, Faculty of Medicine, Federal University of Mato Grosso do Sul, Campo Grande, Brazil
3 Research in Exercise and Nutrition in Health and Sports Performance-PENSARE, Graduate Program in Movement Sciences; Graduate Program in Health and Development in the Midwest Region, Faculty of Medicine, Federal University of Mato Grosso do Sul, Campo Grande, Brazil

Date of Submission25-Jun-2019
Date of Acceptance18-Nov-2019
Date of Web Publication29-Nov-2019

Correspondence Address:
Dr. Hugo A. P. Santana
College of Education, Federal University of Mato Grosso Do Sul, Avenida Costa E Silva, S/N Zipcode 79070-900, Campo Grande, Mato Grosso do Sul
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/CJP.CJP_49_19

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The aim of this study was to identify force–velocity and power–velocity curves in climbing activity protocols, used as dynamic resistance exercise in rats. Eighteen 45-day-old male Wistar rats (weight = 211.9 ± 5.2 g) were evaluated. After familiarization to the climbing procedure, the animals performed an incremental climbing test (load relative to 75% of the body mass at first stage, followed by 30 g increments with and 120 s recovery between climbs) to determine the maximum carrying capacity (MCC). After this, the animals climbed with different loads (without load, 10%, 20%, 30%, 40%, 50%, 75%, 90%, and 100% of MCC) with 120 s recovery between climbs. Time for each climb was recorded to calculate the mechanical power. The peak power was reached at 30% of MCC. For the force–velocity curve, an inversely proportional relation was observed between force and velocity, as expected, greater forces were expressed in lower velocities. Therefore, our results suggest that training at 30% of MCC should be encouraged aiming the target for greater power output and 90%–100% of MCC should be the load aiming for strength training in climbing activities for rats.

Keywords: Animal model, ladder, power–velocity curve, resistance training, strength

How to cite this article:
Santana HA, Miotto H, Silva KK, Dellagrana RA, Almeida JA. Identification of the force–velocity curve on dynamic resistance exercise for rats. Chin J Physiol 2019;62:241-4

How to cite this URL:
Santana HA, Miotto H, Silva KK, Dellagrana RA, Almeida JA. Identification of the force–velocity curve on dynamic resistance exercise for rats. Chin J Physiol [serial online] 2019 [cited 2021 Mar 7];62:241-4. Available from: https://www.cjphysiology.org/text.asp?2019/62/6/241/272025

  Introduction Top

The use of animal models for research is a common practice in the scientific field. Aerobic and resistance exercises performed by animals, especially rodents, have been used in different spectra with several purposes (e.g., changes in the cardiac system, inflammation, and oxidative stress).[1],[2] Animal-based aerobic exercises commonly include treadmill running and swimming with different intensities and volumes. Guidelines for these exercises aim to control speed, intensity, and/or duration.[3] On the other hand, for resistance training, most studies methods show exercises aiming maximal strength, lacking control, or disregarding submaximum training intensities.

Experimental studies with animal models have tried to mimic resistance exercise adaptations, using strategies such as chronic muscle stretching, compensatory overload, and electric stimulation in unconscious animals.[4],[5] Furthermore, some studies include positive and/or negative reinforcement, such as food as a reward or electrical stimulation in the tail to accomplish the activity, respectively.[6] According to Strickland and Smith,[7] more natural experimental models can reach more efficient and reliable data. Thus, ladder-climbing protocols propose normal movement for rodents[8] which are natural climbers, reducing exposures to external factors and simulating resistance exercises without food rewards and electrical stimulation.[9]

With animals, climbing is used as a resistance exercise, which has positive effects using different parameters (i.e., volume, frequency, and intensity).[10] Studies that use ladder-climbing protocols to induce hypertrophy and increase the maximal strength commonly use loads above 50% of the animals' maximum carrying capacity (MCC).[8],[11] On the other hand, to date, resistance training aiming to improve muscle power has shown promising results for several athletic and health parameters in humans.[12],[13] However, to the best of our knowledge, no study with rats aimed to improve muscle power through resistance training using climbing as an exercise.

First, studies with animal models must identify the best parameters of resistance exercise to improve muscle power. Mechanical power is the rate of work or the force multiplied by the velocity of movement.[14] Thus, force and velocity are dependent components in muscular actions. Hill[15] proposed the force–velocity relationship, which presents a hyperbolic model. This premise indicates that an increase in the velocity of movement is accompanied by a decrease of force production capacity during concentric actions. In some dynamic movements (e.g., knee extension, multiarticular movements, jumping, and leg press), the relationship of velocity, force, and tension generated may be different from the hyperbolic proposal, having linear characteristics.[16],[17] Applying these concepts of power and force–velocity that linked to different training intensities seems to be a necessity in resistance training protocols in animal models.[7]

Due to unclear data in the literature related to the optimal load for the muscular power development in rats, the aim of this study was to identify the force–velocity and power–velocity curves in rodents through natural climbing activity to support directions for exercise physiology and training in rats for the best experimental design and load controls.

  Materials and Methods Top


Eighteen male Wistar rats (Rattus norvegicus albinus), with 45 days old, were obtained from the local University of Vivarium. The animals were kept in collective cages (2–3 animals) at a controlled temperature and humidity with 12:12 h dark–light cycles. The animals had ad libitum access to food and water, and all procedures were conducted according to the International Ethical Standards. Further, this study was approved by the Local Ethics Committee of Animal Care (protocol 854/2017).

Exercise adaptation

Although rats are natural climbers, the animals were acclimatized and familiarized with the procedure to minimize any stress responses and other physiological changes related to physical effort. Thus, a simple but essential adaptation was performed.

The animals were familiarized with the environment and the technical apparatus (vertical ladder, 1.1 m, 2.0 cm between steps and 80° of the slope), which consisted of a minimum of three completed sets of climbing the vertical ladder and recovery of the 60s between sets, according to de Cássia Marqueti et al.[9] After the adaptation period to ladder exercise without external load, the animals rested for 48 h. On returning to the climbing protocol, the rats maintained the pattern and performed subsequent climbs without external stimulus. Thus, the animals were considered fit for the incremental test to determine their MCC.

Testing procedures

The incremental test consisted of an initial climb with a load relative to 75% of the animal body mass, attached in a plastic tube fixed to the tail with adhesive tape. After the first climb, a 30 g increment was added to the device. The procedure was repeated until the animal was unable to perform the full climb in the apparatus. The stage was considered complete when the animal ran the entire length of the stairs (1.1 m). The animals recovered 120 s between the climbs.

After the determination of the MCC, the animals climbed with different loads, starting without load and increasing 10% at each climb until reaching 50% of the MCC. After that, the increments were 75%, 90%, and 100% of the MCC according to the protocol suggested by Hornberger and Farrar.[8]

In this procedure, two experienced researchers were responsible for recording time in an individual timer. The timer started measuring when the animal started the climb and stopped when the rat reached the resting apparatus at the top of the ladder. Time (t) was recorded in seconds, and the mean between the two measurements was used for the study analyzes. For reliability measurements, an intraclass correlation coefficient of >0.99 was found between timers.

Therefore, the mean velocity (v) was calculated from the following formula:

1. v = d · t−1,

Where d is the ladder distance (1.1 m).

In physics, Power (P) is the rate of doing work (w), therefore:

2. P = w · t−1

And work can be defined as:

3. w = F ·d

Therefore, applying the formula (3) on (2):

4. P = F ·d · t−1

Using the definition of Force (m · a):

5. P = m · a · d · t−1

Finally, using the formulas for the mean velocity (d · t−1) and substituting acceleration for gravity force (g):

6. P = m · g · v

Hence, the mean power was calculated from the following equation:

7. P = m · 9.81 · v

Where mass (m) is the animal body mass (BM) plus stage load, mean velocity (v) was distance (1.1 m) divided by time (t) recorded from the researchers.

Data analyses

Data are expressed as mean and standard deviation. Graphically, force, mean velocity, and mean power are following 100% (last completed stage), not raw values; therefore, the mean power and mean velocity were identified as a percentage of the MCC. The force–velocity curve was fitted with the averages of force and mean velocities from all animals at their corresponding respective stages.

  Results Top

The animals weighted 211.9 ± 5.2 g and had MCC of 256.8 ± 33.9 g. After the experimental protocol, time and loads were determined and applied in the proposed equations. Force, power, and velocity curves are shown in [Figure 1], which [Figure 1]a demonstrates the force curve increases as the % of MCC increases. In [Figure 1]b, the mean velocity shows a plateau at first stages and then a steady decrease after 30% of MCC. The [Figure 1]c illustrates the peak power at 30% of MCC and a small steady decrease with higher loads. [Figure 1]d shows the force–velocity curve, and as expected, the force is inversely proportional to the mean velocity.
Figure 1: (a) Force at each stage of the incremental test, (b) the mean velocity at each stage of the incremental test, (c) power at each stage of the incremental test, and (d) Force × Velocity curve. BW = Body weight, MCC = Maximum carrying capacity.

Click here to view

  Discussion Top

To the best of our knowledge, this is the first study that has proposed force, power, and velocity curves identification in dynamic resistance training climbing model for rats. The protocol adapted by Hornberger and Farrar[8] has been widely used as a model for strength training of rats.[9],[6] It is a climbing protocol with increasing loads (50, 75, 90 and 100%) of the maximal obtained at an incremental test. In any case, many studies have adopted this model as a method of investigating different goals.[9],[11] Interestingly, contrary to what happened with aerobic exercise models (e.g., running and swimming), little research was performed about the methods of evaluation and training intensities for resistance exercise in animal models.

Effective management control of exercise intensities is a need for any research on humans or animal models. Different exercise training volumes and intensities cause different short and long-term adaptations related to metabolism, strength, fatigue, and body structure.[18] Force–velocity curves have been studied from 1938 to the present, guiding everything from scientists researching isolated muscles up to sports coaches applying different dynamic exercises and intensities in sports training.[15],[19] However, for animal models, especially for resistance training (e.g., ladder), exercise intensity controls are small or poorly reported.

The force–velocity curve had the expected results, showing that under lower forces during the climbing, the animals had higher velocities and vice versa. These occur even with the apparent differences between human and animal models in instructions and automatic movements when performing an exercise. These could influence the curve type. However, it is clear that the velocity reduces at higher forces, showing a linear decrease in the curve. This is similar to some dynamic exercises performed by humans,[16],[17] although it is not a hyperbolic curve, as first shown in the isolated muscle.[15]

Similar to the force–velocity curve analyses, power and peak power should be used to prescribe more effective training directly to the specific goal of the exercise.[12] Different exercise training intensities will lead to different adaptations for power and force output[20] and might play a role in fiber type distribution.[18] The maximum strength seems to influence the percentage of the load to be used to accomplish the peak power.[20] Training mainly in one specific zone of the force curve may shift the curves (force–velocity and power–velocity), and thus, it is necessary to set specific loads to achieve different training goals.

The main limitation of the current study is the method of recording time during climbing (two researchers recorded the time). However, we can highlight that the intraclass correlation coefficient was >0.99 between researchers, indicating reliability in our data. Therefore, using timers to record the climbing times could be a more practical approach regarding training and testing sessions. Furthermore, considering that the climbs analyzed at this research did not have constant acceleration, estimating the power output using an accelerometer coupled to the load carried by rats may provide further insight into this topic. Future research with animal models could benefit from the inclusion of more precise ways to estimate the power output during ladder-climbing training.

  Conclusion Top

The identification of the parameters showed in the present study, although it is model-dependent, guides the intensity control of training sessions, leading to more accurate exercise prescriptions or allowing new experimental designs to be tested in the animal field. Thus, this study should be a guideline for researchers to use different strategies regarding the training intensity for animal models. The findings suggest that training at 30% of MCC should be the target level for accomplishing greatest power and 90%–100% of MCC for strength training zones, which shows the highest applied forces and the mean climbing velocity is the lowest. Future researches should use and compare these different intensities to evaluate long-term changes for strength, power, and general physiological adaptations for climbing training in rats.


This research was financed by the National Council for Scientific and Technological Development and Coordination for the Improvement of Higher Education Personnel.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

  References Top

Guasch E, Benito B, Qi X, Cifelli C, Naud P, Shi Y, et al. Atrial fibrillation promotion by endurance exercise: Demonstration and mechanistic exploration in an animal model. J Am Coll Cardiol 2013;62:68-77.  Back to cited text no. 1
Jones LW, Viglianti BL, Tashjian JA, Kothadia SM, Keir ST, Freedland SJ, et al. Effect of aerobic exercise on tumor physiology in an animal model of human breast cancer. J Appl Physiol (1985) 2010;108:343-8.  Back to cited text no. 2
Kregel KC, Allen DL, Booth FW, Fleshner MR, Henriksen EJ, Musch T, et al. Resource book for the design of animal exercise protocols. Am Physiol Soc 2006.  Back to cited text no. 3
Goldspink DF. The influence of immobilization and stretch on protein turnover of rat skeletal muscle. J Physiol 1977;264:267-82.  Back to cited text no. 4
Roy RR, Meadows ID, Baldwin KM, Edgerton VR. Functional significance of compensatory overloaded rat fast muscle. J Appl Physiol Respir Environ Exerc Physiol 1982;52:473-8.  Back to cited text no. 5
Tamaki T, Uchiyama S, Nakano S. A weight-lifting exercise model for inducing hypertrophy in the hindlimb muscles of rats. Med Sci Sports Exerc 1992;24:881-6.  Back to cited text no. 6
Strickland JC, Smith MA. Animal models of resistance exercise and their application to neuroscience research. J Neurosci Methods 2016;273:191-200.  Back to cited text no. 7
Hornberger TA Jr., Farrar RP. Physiological hypertrophy of the FHL muscle following 8 weeks of progressive resistance exercise in the rat. Can J Appl Physiol 2004;29:16-31.  Back to cited text no. 8
de Cássia Marqueti R, Almeida JA, Nakagaki WR, Guzzoni V, Boghi F, Renner A, et al. Resistance training minimizes the biomechanical effects of aging in three different rat tendons. J Biomech 2017;53:29-35.  Back to cited text no. 9
Giles ED, Jackman MR, MacLean PS. Modeling diet-induced obesity with obesity-prone rats: Implications for studies in females. Front Nutr 2016;3:50.  Back to cited text no. 10
Tibana RA, Franco OL, Cunha GV, Sousa NM, Sousa Neto IV, Carvalho MM, et al. The effects of resistance training volume on skeletal muscle proteome. Int J Exerc Sci 2017;10:1051-66.  Back to cited text no. 11
Loturco I, Suchomel T, Bishop C, Kobal R, Pereira LA, McGuigan M. One-repetition-maximum measures or maximum bar-power output: Which is more related to sport performance? Int J Sports Physiol Perform 2019;14:33-7.  Back to cited text no. 12
Tschopp M, Sattelmayer MK, Hilfiker R. Is power training or conventional resistance training better for function in elderly persons? A meta-analysis. Age Ageing 2011;40:549-56.  Back to cited text no. 13
Kawamori N, Haff GG. The optimal training load for the development of muscular power. J Strength Cond Res 2004;18:675-84.  Back to cited text no. 14
Hill, AV. The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society of London. Ser B-Biol Sci 1938;126:136-95.  Back to cited text no. 15
Finni T, Ikegawa S, Lepola V, Komi PV. Comparison of force-velocity relationships of vastus lateralis muscle in isokinetic and in stretch-shortening cycle exercises. Acta Physiol Scand 2003;177:483-91.  Back to cited text no. 16
Hauraix H, Dorel S, Rabita G, Guilhem G, Nordez A. Muscle fascicle shortening behaviour of vastus lateralis during a maximal force-velocity test. Eur J Appl Physiol 2017;117:289-99.  Back to cited text no. 17
Häkkinen, K. Neuromuscular adaptation during strength training, aging, detraining, and immobilization. Crit Rev Phys Reh Med 1994;6:161-98.  Back to cited text no. 18
Suchomel TJ, Nimphius S, Bellon CR, Stone MH. The importance of muscular strength: Training considerations. Sports Med 2018;48:765-85.  Back to cited text no. 19
Stone MH, O'Bryant HS, McCoy L, Coglianese R, Lehmkuhl M, Schilling B. Power and maximum strength relationships during performance of dynamic and static weighted jumps. J Strength Cond Res 2003;17:140-7.  Back to cited text no. 20


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