HOW MUSCLES WORK

University of Washington

Dept of Physics

 

At the microscopic level muscles are made up of many cylindrical cells called muscle fibers. These fibers are ~50-100 nanometers (10^-9 m) in diameter and several centimeters long.

A typical skeletal muscle consists of many bundles of such fibers arranged in parallel along the length of the muscle. A tiny electrical pulse from a nerve cell attached to the muscle fiber will cause it to contract.

The nerve signal causes the muscle fiber to "twitch". A twitch is a brief contraction and relaxation of the muscle fiber which lasts between about 10 and a few hundred milliseconds, depending on the type of muscle.

If a new nerve signal arrives before the previous twitch has been completed then a stronger contraction will be produced.

High frequency nerve impulses can produce roughly 3.5 times more force than a single twitch.

Each twitch signal will be simultaneously delivered to between 5 and several hundred individual muscle fibers. Muscles which control fine, precise movements will have the smallest number of fibers per nerve (e.g.eyeball muscles).

The combination of a nerve cell and the muscle fibers to which it is attached is called a motor unit. When a muscle first receives a signal to contract only a few motor units respond. Then, if more force is required, more and more motor units are added until the maximum force is achieved. A typical skeletal muscle will have on the order of 300 motor units.

In order to produce a sustained contraction with a constant force the nerves must supply a rapid series of twitch signals so that the individual twitches add and overlap. Thus, when you are holding an object at a constant position your muscle fibers are repeatedly contracting and relaxing in response to a constant barrage of nerve impulses. Each twitch generates some heat and waste products, which is why you get tired even though you are doing no work in the physics sense.

There are basically two types of muscles fibers: "fast-twitch" and "slow-twitch". As the names imply, fast-twitch fibers respond more quickly with stronger contractions, but with a short duration.

Slow-twitch fibers are slower to respond and produce smaller forces, but the forces are applied for longer periods of time.

Also, fast-twitch fibers will tend to become fatigued more quickly than slow-twitch fibers. Most muscles contain a combination of both types of fibers, with the exact mix determined by the use of the muscle. Fast-twitch fibers predominate in muscles used to produce bursts of intense effort, while slow-twitch fibers are more common in muscles where endurance is key.

Slow-twitch fibers tend to be darker in color than fast-twitch fibers, and this is the source of dark and white meat in poultry. Migratory birds like ducks or geese, require lots of high-endurance muscles to fly long distances. Thus, these birds tend to have a higher proportion of dark meat on them than chickens or turkeys.

 

The Law of Muscles:

The force exerted by a muscles depends on the number of muscle fibers being activated. However, the number of fibers in a muscle is fixed at birth; why are some people stronger than others? The strength of an individual muscle fiber depends on its diameter; the bigger, the stronger. Hence, Arnold Schwarzenegger doesn't have more muscle fibers than you do ... his are just bigger.

The force that a muscle can produce depends only on the cross-sectional area of the muscle; not its length.

The result of the Law of Muscles for humans is that human muscles can produce between 30 and 100 newtons of force for every square centimeter of cross-sectional area, regardless of length. A value of ~40 N/cm² is typical for most of the muscles responsible for human locomotion.

1뉴턴은 1kg의 물체에 작용하여 매초마다 1미터의 가속도를 만드는 힘으로, 10만 다인에 해당한다. 기호는 N.

 

More Force Considerations:

The amount of force a muscle can supply depends on the situation.

If a muscle is being stretched (either by another muscle or some outside force) it can exert a force by undergoing eccentric contraction.

This is to be contrasted with concentric contraction, which is the term for the normal situation in which the muscle exerts a force by contracting.

The third possibility is static contraction, in which the muscle exerts a force without changing its length.

Here are some examples to illustrate.

First, imagine you are hanging in some gravity boots and your arms are at your sides. You have a barbell in your hands, which you start to slowly lower towards your face. As you perform this motion, your triceps muscles are stretched longer and longer, and yet they are primarily responsible for supporting the weight. This is an example of eccentric contraction.

The other two are more common and easier to picture.

Now get out of the boots and flip over so you're standing upright. Take the barbell and perform a standard curl. In this case your biceps lifts the weight by contracting; this is concentric contraction.

Now stop curling and hold the barbell steadily in front of you; this is static contraction.

As it turns out, most muscles can exert their maximum force in eccentric contraction. This is why a large backswing is so important in tennis, golf, and baseball batting, etc; by pre-stretching the muscles into a position of eccentric contraction you can maximize their force. If a muscle is pre-stretched by ~20% over its rest length, it will be able to exert about 15% more tension. The extra tension combined with the greater length will translate into about 30% more work. However, the pre-stretch time must be short or the effect is lost; when a golfer backswings her club she doesn't hold it there.

Muscles can typically contract to ~50% of their relaxed length. The speed at which this occurs varies greatly from muscle to muscle (and from species to species). The muscles in the legs of mice can contract at roughly 20 lengths/second while turtle muscles can only contract at 2 lengths/second. Humans are typically in the 4-5 lengths/second range; we're closer to turtles than to mice.

The force a muscle can generate depends on the speed of contraction; the faster the contraction, the less force produced. Hence, the maximum force is produced at zero speed i.e.when the muscle is stationary. This is not very useful for generating motion. The best compromise seems to be at a speed about one third the maximum speed possible. Though this doesn't maximize the force, it does maximize the power output of the muscle.

 

Effects of Fatigue on Muscle:

The molecule which is primarily responsible for providing the energy which drives your muscles is called adenosine triphosphate, or ATP. It's shown to the right; you can see the three phosphates sticking out (each has a P in the middle).

Tiny molecular motors in your muscle fibers use ATP by breaking one of the phosphate bonds, which releases energy and leaves behind---you guessed it---adenosine diphosphate (ADP). If a phosphate is added back onto the ADP it becomes ATP again and can be recycled. However, this takes energy.

Your muscles store very little ATP; about 10-20 seconds of vigorous activity is enough to completely deplete their supply. When this happens the ATP needs to be regenerated or your body will cease to function.

 

There are two primary processes by which the ATP is replenished: the anaerobic cycle and the aerobic cycle.

 

1. The anaerobic cycle (also called glycolysis) uses sugars as an energy source to re-build ATP. Glycogen is stored primarily in the liver, but a small amount is stored in muscle tissue. Glucose is present in the blood. These are the sugars used for glycolysis.

Lactic acid is a by-product of glycolysis. It is often thought of as a waste product from the process of regenerating ATP. However, lactic acid can itself be converted into ATP in the presence of oxygen, so this waste product can also be a fuel. When the body is working anaerobically (using fast-twitch muscle fibers for a burst of extreme activity) lactic acid is made faster than it can be converted to ATP. This is called the anaerobic threshold. After about two minutes above the anaerobic threshold lactic acid will begin to build up.

The first and most obvious result of too much lactic acid in the muscles is an intense, burning pain. This is your body's way of telling you to slow down below the anaerobic threshold so that the lactic acid can be converted to ATP. However, muscle performance does not necessarily degrade at this point. Top athletes can train their muscles to work effectively with elevated lactic acid levels.

Eventually, however, the lactic acid will build up to the point where the blood will become more acidic. This interferes with the chemical reactions that cause the muscles to contract, and performance will quickly degrade until the body starts working aerobically.

2. In the aerobic cycle the energy again comes from glycogen and glucose as well as any lactic acid created anaerobically, but now a new energy source is brought into play: fat. Glycogen dominates for about the first 30 minutes of aerobic exercise and then fat is brought into play.

The body carries glycogen reserves sufficient to last about 1 3/4 - 2 hours of hard running. The fat reserves are generally much greater. One pound of fat contains enough energy to run over 30 miles. However, fat cannot be efficiently utilized without the presence of glycogen. This is the origin of "The Wall" that marathon runners talk about: if they go out too fast they will use up their glycogen in under 2 hours (which is less than it takes to run a marathon) and their muscles won't be able to convert fat efficiently so they will lose energy and not be able to run well.

After about 4 hours of strenuous activity your muscles start to utilize their own proteins as fuel; they essentially begin burning themselves up. After such activity (e.g.an ultramarathon race) studies have shown that the muscles tend to re-build slow-twitch fibers. This is an understandable response; the body is trying to adapt to very long periods of activity. In general the ratio of fast-twitch to slow-twitch fibers that you have is locked in at birth. But this is a way (albeit an extreme one) to alter that ratio later in life ... though it's not highly recommended.

Aerobic activity, then, is the only activity which burns fat. But it does so in a way which may be counter-intuitive. The more intense the activity, the more the muscles tend to utilize the fuel which is close at hand: glycogen. It's only at lower activity levels that fat is burn effectively. For running, fat is burned most effectively when you are going about 30% below your highest sustainable (not sprint) pace. So there's good news and bad news if you want to exercise to lose weight. The good news is that you don't have to kill yourself; moderate activity levels actually burn more fat. The bad news is that there's no quick fix; you don't really start burning fat until after you've been exercising for 30 minutes.

The progressive steps your muscles go through as they fatigue are outlined in the table below.

Time from start of activity	Process	Fuel
0 - 20 s	anaerobic	ATP
20 s - 2 m	anaerobic	glycogen, glucose
2 m - 30 m	aerobic	glycogen, glucose, lactic acid
30 m - 4 hrs	aerobic	glycogen, glucose, lactic acid, fat
>4 hrs	aerobic	fat, muscle protein

 

Aerobic training:

The most basic scale for what your muscles are "used to" are the forces they exert during normal daily activities like walking, etc. Hence, almost any activity that requires motion can be considered aerobic exercise.

The concept of aerobic mile equivalents has been developed to allow people to judge how much exercise they are getting by performing various activities. The idea is to estimate the amount of time that you need to perform a given activity in order to achieve the same health benefit (in terms of increased endurance, etc.) as running a mile.

 

Prolonged aerobic workouts at low force levels will not cause muscles to become bigger and stronger. They will, however, improve endurance and general cardio-vascular health. They do this by improving the blood flow to the muscles (including the heart) by inducing the production of more blood vessels. Having better supply lines improves the ability of the muscles to perform for prolonged periods.

All of this talk about aerobic mile equivalents is fine for the general public trying to stay fit for health reasons.

But there are plenty of athletes who perform in endurance events who need to aggressively improve their aerobic capacity. How should they train?   For serious aerobic training you want to take your body right near the anaerobic threshold and hold it there for a prolonged period (usually 20-60 minutes).

That's all fine and dandy, but how can you tell if you are near the anaerobic threshold? The key is your heart rate.

At low levels of activity your heart rate goes up rapidly as the activity increases. This is because at these low levels all of the activity is aerobic and uses Type I muscle fibers. As more of these fibers are brought into play, more blood and oxygen are required to fuel them so your heart beats faster to keep up with demand.

As the activity level increases, however, your heart rate begins to increase less and less. This is because extreme levels of exertion use fast-twitch fibers that operate anaerobically and so do not require as much excess blood. Hence, if you were to make a plot of your heart rate as a function of exertion level it would increase rapidly at first and then roll over and hit a plateau, where it would remain almost constant. The edge of that plateau is at the anaerobic threshold.

You can estimate where your anaerobic threshold is using the following simple formulas:

HR_max = 220 - age

HR_thresh = A*(HR_max - HR_rest) + HR_rest

where HR_max is an estimate of your safe maximum heart rate (in beats per minute), HR_thresh is an estimate of your heart rate at the anaerobic threshold, and HR_rest is your heart rate when you are resting and relaxed. To determine HR_rest simply find your pulse on your wrist and count beats for 15 seconds, then multiply the result by 4.

The factor A in the equation above is a fudge factor which takes into account what type of person you are and how fit you are. It will range from about 0.55 for puffy, middle-aged business executives to 0.8 for hardened athletes. Though far from exact, these formulas should provide a reasonable estimate of your target heart rate for a maximum aerobic workout. The idea then is to elevate your heart rate to that level (virtually any activity will do) and hold it there for increasing periods. As you train your aerobic threshold will increase; your value of HR_rest will go down, and your value of A will go up.

 

Strength Training:

Serious strength training requires that you push your muscles into the "heavy work load" region of the graph above. And to significantly improve your maximum strength you've got to take your muscles to their very limits. In the short term strength training damages your muscles, even if it is done properly. Over exertion will rupture muscle fibers and cause the muscle to weaken. However, when the fibers heal they will grow back larger and stronger. Hence the key to strength training is proper recovery. This is illustrated below.

This graph plots muscle mass as a function of time through the training cycle. Notice that training actually decreases the muscle mass temporarily. It is only when the muscle is allowed to recover that muscle mass (and strength) increase. If the muscle is trained again before it has fully recovered then it will continue to be damaged and muscle mass will continue to go down, defeating the whole purpose. This is called over-training.

Many techniques and strategies have been developed for strength training...some of the general techniques.

 

ISOMETRIC TRAINING:
It was popularized in the 1950s by Charles Atlas under the name "dynamic tension". The idea of isometric training is to train the muscles using static contraction, i.e.cause the muscle to produce a force without moving. The two primary methods of achieving this are to push against an immovable object (like a wall) or to use muscles against each other so that the flex without bending any joints. This may sound odd at first, but remember that muscles can actually exert their maximum forces when they are not moving. The advantages of isometric training are that it requires no special equipment and can be done virtually anywhere at any time. In practice, however, it has been found that isometric training is not the most effective method of strength training and so it is not used much any more by serious athletes.

 

ISOTONIC TRAINING:
Isotonic training means training the muscles by making them work against a constant force. This is a very common form of training; lifting free-weight barbells is a form of isotonic training.

Though effective, it does have a serious flaw.

The problem is that the maximum force a muscle can exert changes as the muscle changes length. This is illustrated in the graph to the left which shows the max muscle tension as a function of the length of the muscle fibers. Don't worry too much about the details of this graph; the main point is that it is far from a flat line! The reason this is a concern for strength training is that the goal of strength training is to take the muscle to its limit. With isotonic training you can only take the muscle to its limit at the weakest point in the cycle; the muscle will not be at its limit throughout the exercise.

 

 

VARIABLE RESISTANCE:

This training was developed to address this shortcoming of isotonic training. The idea of variable resistance is to change the load force through the exercise to match the force curve of the muscle. Ideally the muscle will be at its maximum force throughout the exercise. There are many different techniques of achieving variable resistance. one of the first and most famous is the Nautilus machine. These machines employ off-center pulleys and cams (which look vaguely like nautilus shells; hence the name) to vary the force needed to support the weight as a function of position. The disadvantage of Nautilus and other similar techniques is that they require lots of large expensive equipment and so are only available at gyms. Each machine is designed for a small number of exercises, and they only effectively exercise the muscles they were designed for. This is used by many free-weight advocates to knock Nautilus machines; with free-weights much more muscle action is required to stabilize the weights laterally and so there is much more indirect training of muscles. It is possible, however, to combine variable resistance and isotonic training to receive the benefits of both techniques.

 

 

 

MAIN POINTS:

Muscle fibers are activated in a fixed order. For an aerobic workout maintain your heart rate at the anaerobic threshold for a prolonged period. In strength training proper recovery is absolutely essential.

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