Length-Force Relationship in Vivo - Lab Report Example

Length-Force Relationship in Vivo I. Introduction One of the key elements for human survival is movement. Movement is defined as “the act or process of moving or change of place or position or posture”. The ability to move within our environment helps us to fulfill our needs and work in our daily lives and the key to human movement is the function of our skeletal muscles. The skeletal muscles, like the joints, are designed to contribute to the body’s needs for mobility and stability. Muscles serve a mobility function by producing or controlling the movement of a bony lever around a joint axis; they serve a stability function by resisting movement of joint surfaces and through approximation of joint surfaces (Levangie & Norkin, 2005). A sound knowledge of its structure, contractile ability and biomechanical characteristics is necessary to understand the interrelationships that determine human function. Diverse but interrelated factors affect the capacity of normal skeletal muscle to generate tension to control the body and perform motor tasks, all of which contribute to the magnitude, duration and speed of force production (Kisner & Colby, 2002). One of the key concepts in the study of muscle contraction is the length-force relationship. Therefore, it is the purpose of this study to understand the length-force relationship in vivo by assessing the torque-angle relationship. This study also aims to determine interrelationship between these two and to determine the different factors affecting force production in skeletal muscles. II. Joint Torque-Angle and Muscle Force-Length Relationships In order to understand skeletal muscle biomechanics, it is important to have a good understanding of its anatomy. The skeletal muscle fibers are made up of contractile myofilaments, actin and myosin as well as the troponin-tropomysin complex. The refractive index differences between these myofilaments are responsible for the striated appearance of skeletal muscle. The light I band, which is composed of the thin filaments actin and the troponin-tropomyosin complex, is divided by the dark Z line and the dark A bands, composed of the thick filament myosin, has the lighter H band in its center. The area between two adjacent Z-lines is called a sarcomere (Ganong, 2003). One of the biomechanical properties important to muscle physiology is the length-force relationship. The force-length relationship of muscle fibers is converted at the joint to a torque-angle relationship. In humans, the torque-angle relationship often is represented as the force-length relationship of muscle fibers (Kawakami & Fukunaga, 2006). Torque, also known as moment of arm, is defined as a measurement of the effectiveness of a force in producing rotation about an axis. It is equal to the product of a force times the perpendicular distance between the site of force application and the axis of rotation (DeLisa, 1998). Torque can also be expressed as: T = Ft sin , where  is the angle between the direction of force application and the axis of rotation (Lieber, 2002). The curves share the same characteristic shape, because the variables graphed on the x and y axes are just scaled versions of length and force, with joint angle replacing the length of the muscle. III. Results Graph 1: Angle-Torque Relationship of the Two Subjects Subject Joint Angle (deg) Muscle Torque (Nm) Tendon Force (Ft, N) Muscle Force (Ff, N) Moment arm (m) Dave 20 79 2468 2626 0.0393 40 155 3647 3880 0.0425 60 226 5433 5780 0.0416 80 227 6840 7277 0.0405 Ayser 20 148 3766 4006 0.0393 40 242 5694 6057 0.0425 60 266 6379 6786 0.0416 80 343 8469 9010 0.0405 Table 1: Tabulated Results The results show that for both subjects, the highest torque produced was at 80 and the least torque produced was at 20. It was observed that the torque produced by the quadriceps was at angles near 90. It was also predicted that a higher moment arm will result in a greater torque production. However, based on the results, this was only evident at 20 knee flexion where the least moment arm also produced the least muscle force. The results for the remaining angles were non-conclusive as the greatest moment arm which was at 60 did not produce the greatest torque. Also, comparing the two subjects, though both almost have similar built, Ayser produced higher results than Dave because he produced a greater muscle force upon knee extension, thereby, generating a greater torque. IV. Discussion As mentioned earlier, in vivo, the length-force relationship in humans is represented by the joint-angle curve. The length-force relationship has a basic shape of an inverted-U and is at the level of the sarcomere. This relationship can be explained by the sliding filament theory. This theory depicts the “cross-bridging” of the myofilaments actin and myosin upon electrical stimulation, also called the excitation-contraction coupling. The cross-bridges are approximately 13 nm long and lie in six rows along the myosin filaments; each row can engage one of the actin filaments in the hexagonal array surrounding the myosin filament. These are arranged in pairs separated by 180 with the next pair 14.3 nm away (McComas, 1996). The cross-bridging occurs with the presence of Ca++ ions, the binding of this to the troponin C causes a conformational change in the troponin-tromyosin complex thereby the uncovering of the active sites in the actin. The myosin heads then attaches to the actin and with the presence of ATP, creates a “power stroke” which pulls the actin filaments together, resulting in the contraction of the sarcomere. The process proceeds again and again until the actin filaments pull the Z membrane up against the ends of the myosin filaments or until the load of the muscle becomes too great for further pulling to occur (Guyton, 2000). The force-length curve has an ascending limb, plateau region and a descending limb. The ascending limb of the force–length relationship is where the active isometric force increases with increasing muscle/fiber length and the descending limb is a region in which the active isometric force decreases with increasing muscle/fiber length (Peterson, Rassier, Herzog, 2004). Similar to the length-tension curve, it states that there is an optimal length wherein the muscle can produce the greatest force, hence called the resting length. The term resting length can be misleading since the muscle can be at rest (relaxed) at many lengths. Thus, the resting length, sometimes called the neutral length, of the intact subject could be considered to be about the midpoint of the joint range or slightly longer (Braddom, 2000). For many, the accepted resting length of a sarcomere is between 2.0 to 2.2 m (Lieber, 1999, Guyton, 2000). The myosin filament is 1.65 μm long and the actin filament is 2.0 μm in length (Lieber, 1999). If the muscle is shortened or lengthened beyond this range, the force of the contraction is greatly reduced. As seen in Fig. 1, the resting length of 2.0 to 2.2 m represents the plateau region. This is where the maximum force contraction is produced because there is maximum overlap between the actin filaments and the cross bridges of the myosin filaments (Guyton, 2000). If the muscle is shortened between 1.0 to 1.5 m, there is a decrease in muscle contraction because it is at this point that the two Z-lines meet the ends of the myosin filaments and the actin filaments overlap both with the opposing actin filament and with the myosin filament. Under these conditions, the actin filament from one side of the sarcomere interferes with cross-bridge formation on the other side of the sarcomere (Lieber, 1999). If the sarcomere is stretched beyond the resting length, it also results in a decreased force production because it does not permit cross-bridging between the actin and myosin filaments to occur since they don’t have little or no point of contact. This explains why shortened (i.e, contractures) or lengthened (i.e, over-stretched) muscles produce less force. Stretching the muscle to the resting length results in the greater force production because of the mechanism explained earlier but also, in addition, to the increase in passive tension of the connective tissue surrounding the muscle, thereby contributing to the total tension produced by the muscle. Fig. 1: Sarcomere length-tension relationship demonstrating active force (heavy line) and passive force (thin line) developed by muscle sarcomeres. [Adapted from Lieber, R. Skeletal Muscle is a Biological Example of a Linear Electro-Active Actuator. Proceedings of SPIE's 6th Annual International Symposium on Smart Structures and Materials, 1-5 March, 1999, San Diego, CA. Paper No. 3669-03. SPIE Copyright 1999] Fig. 2The relationship between joint torque and angles during isokinetic knee extension: a typical result obtained from one subject. On the x-axis, 180° corresponds to full extension of the knee; thus, each movement is performed from left to right. Lines represent different velocities (from top to bottom, 0.52, 1.05, 1.57, 2.09, 2.62, and 3.49 rad·s-1). The instance of peak torque is shown by an arrow for each velocity. [Adapted from Kawakami, Y., K. Kubo, H. Kanehisa, and T. Fukunaga. Effect of series elasticity on isokinetic torque angle relationship in humans. Eur. J. Appl. Physiol. 87:381–387, 2002. Copyright © 2002 Springer Science and Business Media. Used with permission.] A similar study done about the relationship between joint torque and angles during isokinetic knee extension done by (Kawakami, Kubo, Kanehisa & Fukunaga, 2002) yielded the following results in Fig. 2. As seen here, in the ascending limb, less torque was produced in lower angles representing the decrease in initial length. However, as the angle was increased, more torque was produced because of the increase in length thereby increasing the number of cross-bridges. The peak torque was seen between 110 to 130 and this may be indicative of the resting length of the quadriceps. The torque produced beyond this resulted in a decrease in torque, and may be due to the increased length preventing the cross-bridges to occur. Ettema & Kippers (1999) mentioned that the absolute size of the force-length curve is determined by: the physiological cross-sectional area (PCSA), (i.e. number of sarcomeres aligned in parallel), determining the force & the (average) length of the muscle fibers (i.e. number of sarcomeres that are aligned in series), determining the active length range over which a muscle can operate. Muscle force is proportional to PCSA, that is, the greater the cross-sectional area, the greater force that will be produced (Lieber, 2002). It can also be affected by their geometric arrangement, structures of the joint, and the location of the muscles with respect to the joint axis of rotation. Pennation is also another factor since the fiber length of a pennate muscle will be shorter compared with a parallel-fibered muscle. As a consequence, a small change in length of a pennate muscle will result in a reduction in the force developed. However, pennate muscles have a higher PCSA and a greater number of sarcomeres. This will result in a greater force per gram tissue (Narici, 1999). Series elasticity causes a widening of the length-force curve of the muscle-tendon system, without altering its force generating capacity (Ettema & Kippers, 1999). The use of the Cybex machine can be a limitation since the muscle fiber velocity and moment arm are basically never constant during the test so it will be hard to intepret isokinetic data in terms of the muscles generating the torque (Lieber, 2002). Also, the muscle being tested should also be maximally activated for the torque to be measured as the muscle's maximum tetanic force, if not, computations can be regarded as erroneous. Variations in muscle or tendon length during isokinetic movements can also limit the results of this study. Works Cited Braddom, R. L., & Buschbacher, R. M. Physical medicine and rehabilitation. Philadelphia: Saunders, 2000. DeLisa, J. A., & Gans, B. M. Rehabilitation medicine: principles and practice. Philadelphia: Lippincott-Raven, 1998. Ettema, G. & Kippers, V. Muscle Mechanics. School of Biomedical Sciences, Department of Anatomical Sciences, University of Queensland. 17 March 1999 Ganong, William F. Review of Medical Physiology. New York: McGraw-Hill, 2003. Guyton, Arthur C., Guyton-Hall, and John Edward Hall. Textbook of Medical Physiology. Philadelphia, Pa. [u.a.]: Saunders, 2000. Kawakami Y, K Kubo, H Kanehisa, and T Fukunaga. "Effect of Series Elasticity on Isokinetic Torque-Angle Relationship in Humans." European Journal of Applied Physiology. 87. 4-5 (2002): 4-5. Kawakami Y, and T Fukunaga. "New Insights into in Vivo Human Skeletal Muscle Function." 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