Skeletal Muscle Mechanics Length-Tension Curves Lab Report

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Skeletal Muscle Mechanics Length-Tension Curves Lab Report

Skeletal Muscle Mechanics Length-Tension Curves Lab Report



Skeletal muscles are the main organ system that are responsible for movement and force generation. To understand the normal movement of the body parts, a study on the skeletal muscles mechanical properties should be done. The importance of studying the muscle mechanical property stems from the fact that the study leads to the understanding of the normal movement. In this paper an experiment is staged to learn the length-tension characteristic of the skeletal muscles. The paper includes a procedural layout of how the experiment was carried out and the analysis of results. Various measurements were recorded before the final length-tension curve was drawn. From the experiment, it was noted that the change in tension of a muscle results in an increased length of the muscle up to a point where the change in length is zero. At such points, there is no more change on the length as the muscle is stretched to its maximum.

Table of contents

Abstract 2

Table of contents. 3

Introduction. 4

Procedure. 6

Results. 7

Calculations and analysis. 7

Discussion. 10

Conclusion. 11

References. 12


The body muscles are made up of muscle fibers that are bundled up by the use of connective tissues which are attached to the skeletal bones by the use of tendons. During a contraction of muscle fibres, the bone or limb is prompted to move. A single action potential produces a short and weak contraction referred as a twitch. However, a single action potential does not occur because the muscle fibers are organized in such a way that they function cooperatively to produce contractions that are stronger than a twitch (Azeem , 2005).  Latent period is that time between that initiation of the stimulation and the start of the contraction of muscles. The action potential normally occurs at this time, the latent period lasts for about 1 to 2 milliseconds. The contraction time is the time between the onset of contraction and the peak tension. The time is of about 50 millisecond and continues until the all the Ca++ ions are removed. The relaxation time is the time between the peak tension and the complete relaxation of the muscles. It takes about 50 milliseconds or even more. Thus the total time for a contractile response to a single action potential is about100 millisecond, while the action potential that produce the response takes a total time of 2 milliseconds (Carlo, 1992).

The frequency of stimulation is a major factor that influences the tension of whole muscle system. The voluntary stimulation may be a twitch summation, which may be a single action potential, two close action potentials, or multiple action potential. Tetanus is the contraction of maximal strength where many rapid stimuli would prevent muscles relaxation. An increase in action potential equals to an increase maximal strength. This recruits all the fibers and so an asynchronous contraction would not be possible thus causing fatigue eventually. Another factor is the number of muscle fiber that would contract within a muscle.  The length of the fiber at the beginning of the contraction, such as optimal resting length of the muscle would give maximum potential. Lastly muscle tension is influenced by the diameter of the muscle; the bigger the muscle cell, the more they can generate more force (Lieber, 2001; Senden, 2004).

The force developed during an isometric contraction of a muscle varies with the length of the muscle. Isometric contractions are contraction when the muscles are not allowed to shorten. The isometric length tension curves are used to represent the muscle force that can be generated if the muscle is held at series of discrete length. The relationship of muscle length and tension was established through mechanical experiments in the early sixties and basically the length-tension relationship state that isometric tension that generates the muscle is a function of both the magnitude of filaments overlap between the actin and the myosin filaments (Korthuis, 2011). During experiments, isometric contractions are usually done at different lengths while isometric tensions are taken at those lengths.  A theoretical curve of length- tension relationship is as shown in figure 1 below;


Figure 1. Length- tension relationship

Source: (Carlo, 1992)

From the curve, very long and very short lengths muscles would generate very low tensions, and optimal and intermediate lengths of muscle would give higher tension.


The toad sciatic nerve was used in the experiment and the gastrocnemius was arranged to contract isometrically. The setup was kept moist at all times by frequent irrigation with ringer solution. Before the toad nerve or muscle was connected to the transducer, the force transducer was first calibrated using the supplied weights and graph of weight in grams versus displacement mV using a scope on the computer screen. The calibration factors is then calculated and in case any subsequent change in the sensitivity or the baseline it was carefully recorded.

During the setup, the Achilles tendon end of the muscles were then attached to the force transducer and then adjusted to a low tension, which was then measured, treating the voltage as the baseline, the position was also measured. Starting at zero point, the simulator voltage was increased and the nerve was stimulated using single stimuli of 0.2 pulse duration until the maximum twitch tension was recorded. Noting the threshold the following were determined from the trace; the peak twitch tension, time to peak the tension, the latent period and relaxation time. The fact that the tension increases with the stimulus strength up to the maximum fit in with all or none principle was also determined from the trace.

Trains of impulses of increasing frequency were applied and the changes in the muscle tension in summation and tetanus observed. Some of the facts that would be noted include the frequency at which the twitches fuse to produce a tetanic response and later the tetanic tension and twitch tension ratio would be calculated.  In order to create a length a tension curve; the muscle length would be increased by measured stages; the increase made would be 2 turns of the wheel clockwise; 1 turn = 1mm and at each of the position


Calculations and analysis

  • Calibration factor for the force transducer would be given by;

(Y2-Y)/(X2-X1) = (15.43-12.45)/(2.55-2.06) = 6.77mV/N

  • a) The stimulating strength at threshold = 220mV
  1. b) The stimulating strength at the maximal peak twitch tension 190mV

3)         Duration of latent period= 13ms

Duration of contraction phase = 107ms

Half relaxation time=57ms

Peak twitch tension= 2.5637mV

  • Tetanic frequency = 34Hz

Tetanic/ switch tension ratio = 2.5637/3.77= 0.3787 ms

Table 1. The voltage relationship with weight

Displacement in Volts (V)


Weight (kg) Newton (N) Weight
0 0.00 0
0 0.100 0.098 10
3.5 0.150 0.588 60
6.65 0.200 1.078 110
9.46 0.250 1.57 160
12.45 0.300 2.06 210
15.43 0.350 2.55 260
18.23 0.400 3.04 310
21.03 0.450 3.43 350
25.12 0.500 4.02 410




Calibration curve

Figure 2. Graph of voltage against speed

Table 2.Total displacement per force applied

Length Displacement in Volts (V) Weight (kg) Newton (N) Weight


total weight Total Displacement
0 0 0 0 0 0 0
2 0 0.05 0 0 0.05 0.005102
4 0 0.1 0.098 10 110 11.22449
6 3.5 0.15 0.588 60 210 21.42857
8 6.65 0.2 1.078 110 310 31.63265
10 9.46 0.25 1.57 160 410 41.83673
12 12.45 0.3 2.06 210 510 52.04082
14 15.43 0.35 2.55 260 410 41.83673
16 18.23 0.4 3.04 310 310 31.63265
18 21.03 0.45 3.43 350 210 21.42857
20 25.12 0.5 4.02 410 110 11.22449


The length –tension curve for the experiment


Figure 3. Graph of tension per unit total  length



The passive tension length curve would be given by figure 4.

Figure 4. Graph of passive tension against the length of curve


It was noted that the tension in the muscles increases as the strength of the stimulus increases. This finding fits in with the all-or-none principle which states that the strength of response of a nerve or muscle fibre does not depend on the strength of the stimulus. The all-or-none principle, which was formulated in 1871 by Henry Pickering means that a force must always induce a contraction or fail to do so completely. In case the force produces a muscle contraction, it produces the greatest contraction achievable under the prevailing conditions of the muscles (Freeman, 2001).

Earlier literature, (Herzog, 2000; Korthuis, 2011), indicates that the all-or-none principle was initially applicable to the heart muscles only. It was later discovered that all body muscles under stimulation follow the same patterns in their response to stimulating forces. There is a guarantee that once a muscular action is started, it occurs in full magnitude or never occurs at all since there is no information that can get lost along the way. This literature enables us to make the conclusion that any force produced, even in this experiment, either produces muscle contraction or fails to do as completely as shown in the findings in table 2.

The graph of voltage against speed is linear. This shows that an increase in the voltage leads to an increase in the speed of intramuscular contractions. The calibration factor constant is added to the equation and the R2 factor indicates the accuracy of the equation since it tends to unity. The graph of tension versus unit total length, as shown in figure 3, shows that the tension experienced by the muscles is directly proportional to the length of the muscles when a constant increment of force is developed. However, the degree of proportionality reaches a certain limit beyond which any excess tension does not increase the length. Beyond the limit, tension decreases with increase in length.

Interesting observations are made when passive tension is plotted against the length of curve as shown in figure 4. Initially, tension increases rapidly with minimal change in length. The two variables then exhibit direct proportionality. This implies that increase in passive tension leads to an increase in length.

It can be noted that the graph of active tension against length is not the same as that of passive tension against length. The difference occurs where the active tension-length graph shows a higher muscle amplitude response by forming a high crest whereas the passive tension-length graph shows steady relationship. This shows that an electrical signal that is below the threshold strength cannot produce a muscle movement unless it exceeds the threshold point. This fact again concurs with the all-or-none law that has been explained (Kraus, 1995).

From the calculations, it is found that the calibration factor for the force transducer is 6.77mV/N and the tetanic frequency occurs at 34Hz.  This implies that other frequencies are not tetanic but at 34 Hz, the muscles twitch and produce tetanic tension. According to the findings of this experiment, the ratio of tetanic to switch tension is 0.3787 ms.

The second table shows the change of tensional force depending on the calibration factor of the transducer. The total tension was gotten as a summation of the passive tension and the active tension. The total length was taken at steps of two millimeter for every measurement. The graphs show the length tension relationship of the experiment with a total peak tension of 0.38N.


From the experiment we can conclude that the change in tension of a muscle result to an increased length of the muscle up to a point where the change in length is zero and there is no longer change on any length. At this point where the muscle is stretched to its maximum, the muscle is usually fatigued and takes some time to regain its original length.



Carlo, R., 1992. Human anatomy and physiology. 2 ed. Newyork: Springer.

Freeman, G. L. (2001). Studies in muscular tension. S.l.: s.n..

Herzog, W. (2000). Skeletal muscle mechanics: from mechanisms to function. Chichester: Wiley.

Kraus, P., 1995. The Sarcomere Length-Tension Relation, Amsterderm: Universisty of Laiden.

Korthuis, R. J. (2011). Skeletal muscle circulation. San Rafael, Calif.: Morgan & Claypool Life Sciences.

Lieber, R., 2001. Physical Therapy, Singapore: PTJ.

Senden, P. J. (2004). Skeletal muscle characteristics and exercise performance in chronic heart failure. S.l.: s.n.].

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