The Wolff’s Law

I’ve been studying biomechanics these few days, and learned another interesting topic about the bone response to stress.

Wolff’s Law, a widely known bone adaptation theory in the orthopedics, was developed by the German anatomist Julius Wolff in 1892:

The form of a bone being given, the bone elements place or displace themselves in the direction of functional forces and increase or decrease their mass to reflect the amount of the functional forces.

According to Wolff’s Law, bone grows in proportion to mechanical stress. A healthy living bone models and remodels in response to the mechanical stress it experiences so as to produce a minimal weight structure that is adapted to the stresses acted on it.

The changes in bone density, size and shape are the work of two specialized bone cells called osteoblasts and osteoclasts, which respectively form and resorb bone tissue. The bone remodeling occurs throughout life. During the process, resorption precedes formation, so as old bone tissue is replaced by new bone tissue. Remodeling can be in either “conservation mode” with no change in bone mass, or “disuse mode” with a net loss of bone mass characterized by an enlarged marrow cavity and thin cortex. The latter leads to osteoporosis, results from either excessive resorption or inadequate formation. The bone modeling occurs during growth and healing. Unlike remodeling, the osteoblasts predominate the activity (formation) with a net gain in bone mass.

Dynamic mechanical loading causes bones to deform or strain; the larger the loads, the greater the strain. When strain exceeds the remodeling threshold, bone remodeling occurs in conservation mode with balanced resorption and formation. When strain exceeds the higher modeling threshold, the bone modeling occurs, with bone density and mass increased. Disuse mode remodeling is triggered when strain stays below the remodeling threshold, induces a slow loss of bone.

A physically active individual tends to develop denser and more mineralized bones, particularly at the stressed sites. For example, a tennis player has a stronger and denser radius at the racquet-holding arm than the other arm due to the repetitive high stresses exerted on it. Likewise, a trained runner has an increased bone density at the lower extremity due to the high-impact of the running motion. Interesting to note that a competitive swimmer who spends a lot of time in the water however may have less dense bones than a sedentary individual as the buoyant force exerted on the body has counteracted the body weight (gravity).

The law also explains why astronauts suffer from a kind of bone-loss similar to osteoporosis after a long stay in space. Due to the microgravity, the floating human body undergoes a weightless and almost immobile condition. Since no weight is acted on the skeleton and the body do not have to fight the gravity to move about, the bone mass diminishes, hence the strength and the bone mineral density decrease. Bedridden patients and individuals who lead a sedentary or inactive lifestyle tend to have a decrease in bone mass too as a result of reduced mechanical stress and weightbearing activity. The bones become more susceptible to fractures.

In many traditional Okinawan karate-do and Chinese martial arts, body conditioning is crucial as part of the training routine to strengthen muscles and bones, as well as to elevate the pain threshold. Uechi-ryu karate-do emphasizes conditioning on knuckles, forearms, abdomen, tips of toes, dorsal feet, shins, thighs and calves by repetitively blocking and striking the areas to produce slight trauma to them. Other practices like rubbing, knuckle push-ups, rolling a stick on the shin are formulated for conditioning purpose as well. The principle founded by the ancient Chinese masters is the same as the Wolff’s law theory: the bones become denser and stronger after bearing a long period of dynamic mechanical loadings provided by the body conditioning, thus minimize the possible injuries caused by training and sparring.

However, if the applied mechanical loadings are beyond the power of (re)modeling, it leads to fatigue or stress fractures. This problem is very common to athletes who run and jump on the hard surfaces such as distance runners, basketball players, and ballet dancers. The most common affected bones are femur, tibia, navicular and metatarsals. Similarly, martial artists who overtrain themselves may encounter the same problem, when the stresses applied to the bone exceed the bone’s ability to adapt. Therefore it is important for martial artists to ensure the training is done within safe bounds.