## Internal Forces and the Human Body Complexity of the Musculoskeletal System

6.1 Introduction

External forces that act on a body induce physical stresses within the body. These stresses have wide-ranging consequences. The gravity causes com-pressive stresses in our musculoskeletal system, slowly shortening us as we get older. An accidental fall could induce such high-level stresses in a bone that it could fracture. Even without the application of an external force, an object can be under stress. Consider, for example, a thick rubber tube that is free of loading, except the action of gravity. Let us invert the rubber tube such that the inner cylindrical surface becomes outer and vice versa. At this configuration, the tube is stressed; the outer layer is under tension and the inner layer is under compression. Similar to the inverted cylindrical tube, ringlike specimens of animal aortas spring open after being cut in the radial direction, indicating that natural configuration of some biological tissues is not stress free.

Regardless of the state of motion, external forces acting on a body will cause internal stresses within the body. It is impossible to directly determine the system of forces carried by the muscles, the ligaments, and the joint articular surfaces in the human and animals. There is much redundancy in the human animal structure. The number of load-transmitting elements at a joint almost always exceeds the number of equations governing the motion of that joint. Consider for example the human knee shown in Fig. 6.1. This joint has a multitude of ligaments that hold it together and a large number of muscles acting on it. Even in the simplest weight-lifting exercises, multiple muscles will contribute to the lifting of the weight. How do we estimate the forces carried by various ligaments, muscles, and bones, given the external forces acting on the body?

The first step is to draw a free-body diagram of a body part in which all forces acting on it are clearly laid out. Then, one considers the equations of motion (or static equilibrium) to compute the unknown forces shown in the diagram. Typically, the unknown forces carried by a passive structures (capsules, ligaments, and the bones) intersecting at a joint

(a) knee, posterior, extended medial meniscus tibial collateral ligament

(a) knee, posterior, extended medial meniscus tibial collateral ligament

posterior cruciate ligament

anterior cruciate ligament posterior meniscofemoral ligament lateral meniscus

(b) knee, sagittal

fibular collateral ligament popliteus quadriceps anterior cruciate ligament posterior meniscofemoral ligament lateral meniscus fibular collateral ligament popliteus

patellar ligament iliotibial tract quadriceps bursa patella patellar ligament iliotibial tract

Figure 6.1a,b. The lateral view of the knee joint (a, posterior; b, sagittal) and some of the ligaments associated with it.

are lumped together and denoted as the total joint force. In the presence of large muscle moments acting on a joint, the moment created by passive structures on the rotational center of the joint may be negligible. This is however not true during impact loading where ligaments are maximally stressed to keep the joint intact.

In allocating forces to various muscle groups involved in posture, movement, and motion, two general approaches have been usedâ€”the reduction method and the optimization method. In the optimization technique, one assumes that muscles exert forces on bones near joints according to the minimization of some performance criterion. A large number of optimization criteria, including ad hoc principles of minimal muscle force, minimal muscle stress, and minimal energy expenditure or consumption, have been utilized. The method is attractive because sequences of movement in locomotion appear to suggest an intrinsic optimization process achieved through learning. This point can be illustrated with the consideration of vertical jumping where the position of the upper body is determined by the angles at the hip, knees, ankles, and metatarsal heads. The system has four degrees of freedom and thus our body allows the jumping task to be executed in a variety of ways. Yet, after practice, most movement tasks that lead to jumping seem to be performed in stereotyped manners. The sequence of muscular activation appears to be always in the order of upper body, upper legs, lower legs, feet, suggesting an optimization process. The biomechanics literature contains many examples of the application of optimization techniques in the study of the shoulder, hip, and knee. See review arti cles on the subject for further exploration of the merits and weaknesses of this approach.

The method of reduction is much simpler mathematically than the method of optimization. It is essentially the reduction of the number of unknown forces acting at a joint to a number of available equations of mechanics. Electromyographic (EMG) signals are often used as guides to choose muscles that actuate a certain movement. A common assumption in calculating the force produced by the agonist is to set the force produced by antagonistic muscles equal to zero. This results in a low estimate of the muscle force produced by the agonist. Despite the rather drastic simplifications one has to make in using the reduction method, it does provide insights into the mechanical function of various muscle groups. In many instances, the method actually captures the essence of the human body mechanics. The next section presents examples of the method of reduction in the study of muscle force during movement.