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Muscle Force Length Relationship Definition Essay

The length-tension relationship is the observation that the isometric force exerted by a muscle is dependent upon its length when tested.

The length-tension relationship can likely be explained by interactions between two underlying mechanisms: the active and passive length-tension relationships.

The active length-tension relationship reflects the degree of overlap between the actin and myosin filaments in a sarcomere. Too much or too little overlap leads to sub-optimal tension being developed but where the overlap is “just right” maximal tension is developed.

The passive length-tension relationship reflects the presence of elastic elements within a sarcomere, which stretch and produce force with increasing length.

The length tension relationship describes the force exerted by individual muscle fibers or muscles. It does not describe the torque exerted by a joint at different angles. This is called the torque-angle relationship.

Contraction type markedly affects the angle of peak torque, and it moves to longer lengths in eccentric contractions compared to in concentric contractions. This could be either because of the unique behavior of titin in eccentric contractions, or because of the superior rapid force development in concentric contractions.

The angle of peak torque is often increased to reflect a longer muscle length following a strength training intervention. The effects of muscle length during strength training on angle of peak torque are unclear, but longer muscle lengths may lead to greater shifts in the angle of peak torque.

Muscle fascicle length does tend to increase after strength training, particularly after eccentric training.  The effects of muscle length during strength training on angle of peak torque are unclear, but longer muscle lengths may lead to greater increases in muscle fascicle length.

The relationship between the change in the angle of peak torque after strength training and the increase in muscle fascicle length is unclear, but there does appear to be a moderately-strong relationship, at least after eccentric training. This suggest that an increase in muscle fascicle length is partly (but not wholly) responsible for the change in the angle of peak torque.

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CONTENTS

Full table of contents

  1. The length-tension relationship
  2. The torque-angle relationship
  3. Changing the length-tension relationship
  4. References
  5. Contributors
  6. Provide feedback

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THE LENGTH-TENSION RELATIONSHIP

PURPOSE

The purpose of this section is to provide a short description of the length-tension relationship and details of the current theory by which it arises.

INTRODUCTION

The length-tension relationship

The length-tension relationship describes the phenomenon whereby a muscle or single muscle fiber displays different levels of maximum isometric force production depending on the length at which it is tested (Gordon et al. 1966). It is thought that this phenomenon is related to the extent to which the individual sarcomeres within the muscle fiber are overlapping (Brughelli & Cronin, 2007). There are two key parts to the length-tension relationship:

  1. the active length-tension relationship, and
  2. the passive length-tension relationship.

The active length-tension relationship

The active length-tension relationship is thought to occur as a result of the degree of overlap between the actin and myosin filaments within an individual sarcomere (Gordon et al. 1966). Too much or too little overlap leads to sub-optimal tension being developed but where the overlap is “just right” the maximal tension is developed. The following chart shows a theoretical relationship between the tension developed by a sarcomere at different lengths, leading to different degrees of overlap:

Diagram showing the active length-tension relationship

Explanation of active length-tension diagram

The following key points can be observed on the diagram:

Ascending limb (between 1.3μm and 2.0μm) – in this section, the force expressed by the sarcomere increases rapidly with increasing sarcomere length.  In this section, the actin and myosin filaments are so overlapped that they interfere with neighboring sarcomeres and reduce the potential for strength expression.

Plateau (between 2.0μm and 2.2μm) – in this section, there is no change in force with increasing length as no additional cross-bridges can be formed.

Descending limb (between 2.2μm and 3.6μm) – in this section, there is decreasing overlap between actin and myosin filaments and therefore the force that the sarcomere is capable of expressing decreases with increasing length.

Beyond descending limb (>3.6μm) – in this section, there is no overlap between actin and myosin filaments. Therefore, no myosin cross-bridges are close enough to the actin active sites in order to bind with them and so no force generation can occur.

The passive length-tension relationship

The passive length-tension relationship is thought to occur much more simply as a result of the elastic elements within a sarcomere, within a muscle fiber and within the muscle itself. Thus, the passive length tension relationship is largely unnoticed at small muscle fiber lengths but becomes very important very quickly once the muscle is stretched beyond a certain length. The following chart shows a theoretical relationship between the passive tension developed by a sarcomere at different lengths, leading to steadily increasing elastic force with increasing length:

Diagram showing the passive length-tension relationship

Explanation of passive length-tension diagram

The following key points can be observed on the diagram:

Below 2.2μm – in this section, which is below the optimum length of the muscle is exceeded, the passive tension exerted by a sarcomere is practically zero.

Above 2.2μm – in this section, the force exerted by the passive structures within the sarcomere increases exponentially. Passive forces arise for various reasons, including the role of titin within the sarcomere but also because of other elastic structures, such as connective tissue.

The combined length-tension relationship

The combination of the active and passive length-tension relationships explains the overall length-tension relationship. Overall, where the active length-tension relation predominates (i.e. at short lengths), the curve rises, plateaus and then falls back down. The rising part of this section is known as the “ascending limb” and the falling part is known as the “descending limb”. The following chart shows a theoretical relationship that combines the active and passive length-tension relationships:

Diagram showing the combined active and passive length-tension relationship

SECTION CONCLUSIONS

The length-tension relationship is the observation that the isometric force exerted by a muscle is dependent upon its length when tested.

The length-tension relationship can likely be explained by interactions between two underlying mechanisms: the active and passive length-tension relationships.

The active length-tension relationship reflects the degree of overlap between the actin and myosin filaments in a sarcomere. Too much or too little overlap leads to sub-optimal tension being developed but where the overlap is “just right” maximal tension is developed.

The passive length-tension relationship reflects the presence of elastic elements within a sarcomere, which stretch and produce force with increasing length.

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THE TORQUE-ANGLE RELATIONSHIP

PURPOSE

The purpose of this section is to provide a short description of the torque-angle relationship of joints and how it differs from the length-tension relationship of single muscle fibers.

INTRODUCTION

The torque-angle relationship

[Read more about: the torque-angle relationship]

Importantly, the length tension relationship describes the force exerted by individual muscle fibers or muscles at different lengths. It does not describe the isometric torque exerted by a joint at different angles in a joint range of motion. This is called the torque-angle relationship. In any joint range of motion, there is an angle of peak torque (also called the optimum angle) as shown in the chart below.

The torque-angle relationship, and therefore the angle of peak torque, can be affected by a range of factors that do not impact the length tension relationship of individual muscle fibers or muscles, including:

  • the moment arm length of the muscle,
  • the prevailing normalized fiber lengths,
  • regional muscle cross-sectional area,
  • tendon stiffness,
  • muscle stiffness, and
  • joint angle-specific levels of neural drive.

The length-tension relationship and the torque-angle relationship

Even though there is a difference between the length-tension relationship and the torque-angle relationship, many investigations of the length-tension relationship proceed by exploring differences in maximum voluntary isometric contraction (MVIC) torque with changing joint angle. In such cases, joint angle is taken as a proxy for muscle length and joint torque is taken as a proxy for muscle force. However, great care should be taken in interpreting the results of these studies, as we cannot draw inferences about the length tension relationship directly from the torque-angle relationship, unless the other factors that influence the torque-angle relationship are controlled for.

Effect of contraction type on the torque-angle relationship

The length-tension relationship has been primarily studied during isometric contractions, while the torque-angle relationship has been explored in both isometric and isokinetic (eccentric and concentric) contractions. Importantly, the angle of peak torque differs between eccentric and concentric contractions, for the exact same joint angle movement. For example, Melo et al. (2016) investigated eccentric and concentric knee extension and knee flexion exercises and showed that the eccentric versions involved an angle of peak torque at longer muscle lengths (later in the eccentric movement) than in the concentric equivalents.

There are several features of each contraction type or “mode” that could explain why the torque-angle relationship varies when studied under each condition. Firstly, eccentric contractions make greater use of titin, which is a giant molecule found inside muscle fibers that increases passive tension during (active) lengthening. This could easily increase the force that is produced at longer lengths (but not at shorter lengths), and thereby shift the angle of peak torque during eccentric contractions to longer lengths compared to in concentric or isometric contractions. Secondly, through neural mechanisms, concentric contractions are able to make greater use of their maximum available force-producing capacity during the early phase of contractions, compared to both eccentric and isometric contractions (Tillin et al. 2012). This could increase the force produced at shorter lengths (compared to at longer lengths), and thereby shift the angle of peak torque during concentric contractions to shorter lengths compared to in eccentric or isometric contractions.

SECTION CONCLUSIONS

The length tension relationship describes the force exerted by individual muscle fibers or muscles. It does not describe the torque exerted by a joint at different angles. This is called the torque-angle relationship.

Contraction type markedly affects the angle of peak torque, and it moves to longer lengths in eccentric contractions compared to in concentric contractions. This could be either because of the unique behavior of titin in eccentric contractions, or because of the superior rapid force development in concentric contractions.

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CHANGING THE LENGTH-TENSION RELATIONSHIP

PURPOSE

The purpose of this section is to provide a short description of how the length-tension relationship can be changed, both acutely and in long-term training interventions.

BACKGROUND

Changes in the angle of peak torque can be observed after both acute exercise (i.e. a single workout) and after long-term training (Brughelli & Cronin, 2007). It is currently still unclear whether the changes after acute exercise and after long-term training are caused by the same, similar, or different factors.

ACUTE IN VIVO INVESTIGATIONS

Introduction

Temporary shifts in the angle of peak torque towards longer muscle lengths have often been observed after acute exercise. Originally, such observations were made only after bouts of eccentric training (Brughelli & Cronin, 2007). However, more recently studies have found that workouts involving only concentric training are also able to produce shifts in the angle of peak torque to longer muscle lengths (Guex et al. 2013; Coratella et al. 2015; 2016).

Mechanisms of effect

The mechanisms by which acute exercise produces changes in the angle of peak torque towards longer muscle lengths are unclear. Early in vitro studies found that subjecting muscle fibers to eccentric contractions shifts the point at which maximum force is developed to longer muscle fiber lengths (Wood et al. 1993; Morgan et al. 1996; Talbot & Morgan, 1996; Butterfield & Herzog, 2005). Similar acute effects occur in relation to the angle of peak torque (Brughelli & Cronin, 2007). The lengthening (eccentric) aspect of the contraction was once thought to be important for the shift in the angle of peak torque, so it was believed that the mechanism by which the shift occurred was related to muscle damage an increase in non-uniform sarcomere behaviors (Gregory et al. 2007). However, markers of muscle damage are not related to the extent of the change in the angle of peak torque after exercise (Welsh et al. 2015), and eccentric contractions are not necessary for an acute shift in the angle of peak torque (Guex et al. 2013; Coratella et al. 2015; 2016). Indeed, Guex et al. (2013) showed that fatigue was likely partly responsible for the shift in the angle of peak torque, while concentric training at long muscle lengths was also partly responsible, potentially by causing muscle damage.

LONG-TERM IN VIVO INVESTIGATIONS

Introduction

Studies have often been performed to assess the effects of long-term strength training programs on either the angle of peak torque (also called the optimum angle), or on changes in muscle fascicle length, or both. Where such studies have been carried out, they have most commonly used eccentric training. However, some investigations have also used isometric contractions, coupled eccentric-concentric or stretch-shortening cycle contractions, and concentric-only contractions as well.

Effects of strength training on angle of peak torque

Studies have often shown that the angle of peak torque is increased to reflect a longer muscle length following a strength training intervention (Whitehead et al. 1998; Bowers et al. 2004; Philippou et al. 2004; Clark et al. 2005; Chen et al. 2007; Yeung and Yeung, 2008; Brughelli et al. 2010; Alegre et al. 2014). This increase in the angle of peak torque after training is often taken to reflect an increase in the muscle fascicle length as a result of sarcomerogenesis, but since the angle of peak torque is not identical to the length tension relationship, other factors could also have an impact.

Effects of muscle length during strength training on angle of peak torque

ISOMETRIC STUDIES

Some studies have compared the effects of different types of strength training on the change in the angle of peak torque. Isometric training is the easiest way to assess the effects of training at either long or short muscle lengths (Alegre et al. 2014; Noorkõiv et al. 2015). These studies have found conflicting results. Alegre et al. (2014) reported that isometric training at long muscle lengths led to an increase in the angle of peak torque to longer muscle lengths, while isometric training at short muscle lengths led to a decrease in the angle of peak torque to shorter muscle lengths. On the other hand, Noorkõiv et al. (2015) reported that there was no effect of training on the angle of peak torque in either group.

DYNAMIC STUDIES

Comparing dynamic training at long and short muscle lengths, McMahon et al. (2014) used a range of exercises in which the subjects performed either full or partial ranges of motion. In the short muscle length group, the angle of peak torque reduced slightly to a shorter muscle length (from 75 to 70 degrees). In the long muscle length group, the angle of peak torque did not change after training. In another study design, Guex et al. (2016) used the biarticular nature of the hamstrings to train the muscles eccentrically at either long or short muscle lengths. The subjects in both groups trained using knee flexion muscle actions, but one group performed the exercise lying down, with the hip in 0 degrees of flexion (full extension), while the other group performed the exercise seated, with the hip in 80 degrees of flexion. The angle of peak torque tended to shift to longer lengths in both groups, but the shift was much greater in the group that trained at a longer muscle length (17.3 vs. 8.8 degrees).

Effect of strength training on muscle fascicle length

[Read more: muscle architecture]

Muscle fascicle length does tend to increase after strength training, particularly after eccentric training. Some studies in trained subjects have not found significant increases in fascicle length as a result of strength training interventions (Blazevich & Giorgi, 2001; Blazevich et al. 2003; Nimphius et al. 2012). However, many studies in untrained individuals have reported increases in muscle fascicle length (Seynnes et al. 2007; Reeves et al. 2003; Alegre et al. 2006; Blazevich et al. 2007; Reeves et al. 2009; Potier et al. 2009; Duclay et al. 2009; Baroni et al. 2013; Kim et al. 2014; McMahon et al. 2014). However, a minority of trials have also reported no increases (Kawakami et al. 1995; Duclay et al. 2009; Erskine et al. 2010; Raj et al. 2011; Guilhem et al. 2012; Scanlon et al. 2013; Alegre et al. 2014).

Effects of muscle length during strength training on fascicle length

ISOMETRIC STUDIES

Some studies have compared the effects of different types of strength training on the change in muscle fascicle length. Isometric training is the easiest way to assess the effects of training at either long or short muscle lengths (Alegre et al. 2014; Noorkõiv et al. 2015). These studies have found similar results. Alegre et al. (2014) reported that fascicle length remained unchanged in both groups, even though there was a change in the angle of peak torque in the group that trained at long muscle lengths. Noorkõiv et al. (2015) reported that both groups increased muscle fascicle length similarly. Thus, these studies suggest that the length of the muscle during strength training may not be an important factor for altering muscle fascicle length, at least when using isometric contractions.

DYNAMIC STUDIES

Comparing conventional free weight, dynamic training at long and short muscle lengths, McMahon et al. (2014) used a range of exercises in which the subjects performed either full or partial ranges of motion. In the long muscle length group, muscle fascicle lengths increased 23 ± 5%, while in the short muscle length group, muscle fascicle length only increased by 10 ± 2% over the same period. Comparing the effects of eccentric training at long and short muscle lengths, Guex et al. (2016) found that muscle fascicle length increased in both groups, but the increase was greater in the group that trained at long muscle lengths than in the group that trained at short muscle lengths (9.3% vs. 4.9%). Moreover, there was a moderate correlation between the change in muscle fascicle length and the change in the angle of peak torque when measured concentrically (r = 0.57) but not when measured eccentrically (r = 0.17). This suggests that increases in muscle fascicle length are partly responsible for the change in the angle of peak torque after strength training, although other factors are likely involved.

SECTION CONCLUSIONS

The angle of peak torque is often increased to reflect a longer muscle length following a strength training intervention. The effects of muscle length during strength training on angle of peak torque are unclear, but longer muscle lengths may lead to greater shifts in the angle of peak torque.

Muscle fascicle length does tend to increase after strength training, particularly after eccentric training.  The effects of muscle length during strength training on angle of peak torque are unclear, but longer muscle lengths may lead to greater increases in muscle fascicle length.

The relationship between the change in the angle of peak torque after strength training and the increase in muscle fascicle length is unclear, but there does appear to be a moderately-strong relationship, at least after eccentric training. This suggest that an increase in muscle fascicle length is partly (but not wholly) responsible for the change in the angle of peak torque.

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REFERENCES

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CONTRIBUTORS

Chris Beardsley performed the literature reviews, wrote the first draft of this page and was the primary author.


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Top· Contents · References

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