Length-tension relationship

In skeletal muscles

Tension in muscles is composed of the forces generated by many cross-bridge formations. It is the pulling of the actins by myosin heads towards each other that exerts this tension. The magnitude of the tension depends on the frequency of the stimulation and the initial resting length of muscle fibres, of which will be discussed now. Keep in mind that muscle fibres are composed of many sarcomere units. The length of the sarcomeres dictates the overall length of a muscle fibre.

Graph 1. Length-tension relationship of sarcomeres presented in a graphical form.

At 1 on Graph 1, the sarcomere is overly contracted at rest. There is a high degree of overlap between the thin and thick filaments. Muscle contraction causes actin filaments to slide over one another and the ends of myosin filaments. Further muscular contraction is halted by the butting of myosin filaments against the Z-discs. Tension decreases due to this pause in cross-bridge cycling and formation.

As the resting muscle length increases, more cross-bridges cycling occurs when muscles are stimulated to contract. The resulting tension increases. Maximum tension is produced when sarcomeres are about 2.1 to 2.2 μm long, as seen in 2. This is the optimal resting length for producing the maximal tension.

By increasing the muscle length beyond the optimum, the actin filaments become pulled away from the myosin filaments and from each other. At 3, there is little interaction between the filaments. Very few cross-bridges can form. Less tension is produced. When the filaments are pulled too far from one another, as seen in 4, they no longer interact and cross-bridges fail to form. No tension results.

This principle demonstrates the length-tension relationship. Maximal tension is readily produced in the body as the central nervous system maintains resting muscle length near the optimum. It does so by maintaining a muscle tone, i.e. muscles are contracted partially. The myofilaments are also elastic. They maintain enough overlap for muscular contraction.

In cardiac muscles

The length-tension relationship is also observed in cardiac muscles. However, what differs in cardiac muscles compared to skeletal muscles is that tension increases sharply with stretching the muscle at rest slightly. This contrasts with the gradual build up of tension by stretching the resting skeletal muscle (see Graph 4). This may be due to high senstivity of cardiac muscles to Ca²⁺ or the increase in sarcomere length increases tension on stretch-activated Ca²⁺ receptors, propagating further Ca²⁺-induced Ca²⁺ release due to the increase of Ca²⁺ from the aforementioned Ca²⁺ receptors.

Graph 2. Length-tension relationship observed in cardiac muscles.

The optimum length is denoted as L_max which is about 2.25μm, as shown on Graph 2. Like skeletal muscles, the maximum number of cross-bridges form and tension is at its maximum here. Beyond this, tension decreases sharply.

In normal physiology, L_max is obtained as heart ventricles become filled up by blood, stretching the myocytes. The muscles then converts the isometric tension to isotonic contraction which enables the blood to be pumped out when they finally contract. The heart has an intrinsic control over the stroke volume of the heart and can alter the force of blood ejection.

Force-velocity relationship

Cardiac muscle has to pump blood out from the heart to be distributed to the rest of the body. It has 2 important properties that enable it to function as such:

• It carries a preload, composed of its initial sarcomere length and end-diastolic volume. This occurs before ejecting blood during systole. This is consistent with Starling's law which states that:

"the mechanical energy set free in the passage from the resting to the active state is a function of the length of the fibre."

- Boron et al. (2009, p. 547)

• It has to overcome the afterload, which is the arterial pressure that opposes blood outflow from heart.

Graph 3. Force-velocity relationship in cardiac muscles.

At rest, the greater the degree of initial muscle stretch, the greater the preload. This increases the tension that will be developed by the cardiac muscle and the velocity of muscular contraction at a given afterload will increase. Upon stimulation of cardiac muscle, it develops isometric tension without shortening. Once enough tension has accumulated, the muscle can now overcome the afterload and eject the blood it was carrying. Tension however is maintained at this stage.

When the afterload is so large no shortening can occur (as shown on Graph 3 when velocity is at 0 mm/sec at the x-axis; also marked by P₀), the afterload forms the isometric tension. Tension is greater in muscle stretched more initially as the preload at a given velocity for muscular shortening. The same muscle with a shorter resting length has a lower tension in comparison. These observations are consistent with the length-tension relationship.

At the hypothetical maximum velocity of shortening (marked V_max on Graph 3), muscular shortening is consistent and contracts at the fastest rate when there is no afterload.

Sarcomeres with slightly different properties!

(Graph 4 - Comparison of length-tension relationships between skeletal muscle sarcomeres and cardiac muscle sarcomeres.)

References

• Graph 1 adapted and modified from Martini (2001, p. 115)
• Graphs 2 and 3 adapted from Cambray-Deakin et al. (2011, p. 14-15)
• Graph 4 adapted from Boron et al. (2009, p. 546)