# Limit to Functional Hypertrophy?

The question is this: Is there a point where adding more muscle bulk on will not lead to greater contractile strength in a muscle? Assuming, of course, idealized nervous response. I know Bompa states directly that contractile strength is directly proportional to muscular cross section, but I have been questioning that from a physical standpoint.

My basis for skepticism here is geometric: The first muscle fiber which runs essentially straight from the insertion point to the insertion point, and meets the insertion point at a 90 degree angle. The next muscle fiber will have the belly deflected by the thickness of a fiber (t), and will thus meet the insertion point at a small angle (a).

If we assume all fibers are capable of similar contractile force F, and all fibers have the same diameter, and that those fibers are incompressible we see:

(Total Force) = Sum (F*cos(a))

For a round muscle of length L, with fibers of thickness t, we can approximate

(Total Force) = Sum ( (FL/2) / ((nt)^2+(L/2)^2)^0.5 )

Where n is the number of fibres between the fiber of interest and the center of the muscle.

The first thing we can see in this formula is that the further away from the center of the muscle the fiber is, the less contractile force it is contributing. Is this decrease significant? To determine this properly I would need to know the thickness, length, contractile force and compressibility of the underlying muscle. This leads us to the problem where a muscle fiber could, theoretically, contract and pull itself lower into the underlying fibers, reducing its arc-length, leaving it?s contractile force dependant on the solidity of the underlying muscle. The more solid (and friction free!) the surface, the more force it will transfer. The softer the underlying muscle, the less force will be transferred, and the more of the peak of the muscle will flatten out.

Another interesting corollary that a longer muscle should be slightly stronger than a shorter muscle of the same cross section. Essentially it would transfer the tension to the tendon more efficiently.

If you want to play with this sort of geometry grab the rope-attachment on the cable-row, and play around with narrower and wider grips. You can easily see how much more tension you need in the rope in order to pull the same weight with your hands further apart.

To the original point: Is it possible to build a muscle fiber which is so arched that it does not contribute appreciably to the strength of a contraction? Bompa could certainly be correct given certain characteristics of muscle, which I have to go off and look up now.

Dammit Jim, I’m a physicist not a biologist!

[quote]W.E.C wrote:
The question is this: Is there a point where adding more muscle bulk on will not lead to greater contractile strength in a muscle? Assuming, of course, idealized nervous response. I know Bompa states directly that contractile strength is directly proportional to muscular cross section, but I have been questioning that from a physical standpoint.

My basis for skepticism here is geometric: The first muscle fiber which runs essentially straight from the insertion point to the insertion point, and meets the insertion point at a 90 degree angle. The next muscle fiber will have the belly deflected by the thickness of a fiber (t), and will thus meet the insertion point at a small angle (a).

If we assume all fibers are capable of similar contractile force F, and all fibers have the same diameter, and that those fibers are incompressible we see:

(Total Force) = Sum (F*cos(a))

For a round muscle of length L, with fibers of thickness t, we can approximate

(Total Force) = Sum ( (FL/2) / ((nt)^2+(L/2)^2)^0.5 )

Where n is the number of fibres between the fiber of interest and the center of the muscle.

The first thing we can see in this formula is that the further away from the center of the muscle the fiber is, the less contractile force it is contributing. Is this decrease significant? To determine this properly I would need to know the thickness, length, contractile force and compressibility of the underlying muscle. This leads us to the problem where a muscle fiber could, theoretically, contract and pull itself lower into the underlying fibers, reducing its arc-length, leaving it?s contractile force dependant on the solidity of the underlying muscle. The more solid (and friction free!) the surface, the more force it will transfer. The softer the underlying muscle, the less force will be transferred, and the more of the peak of the muscle will flatten out.

Another interesting corollary that a longer muscle should be slightly stronger than a shorter muscle of the same cross section. Essentially it would transfer the tension to the tendon more efficiently.

If you want to play with this sort of geometry grab the rope-attachment on the cable-row, and play around with narrower and wider grips. You can easily see how much more tension you need in the rope in order to pull the same weight with your hands further apart.

To the original point: Is it possible to build a muscle fiber which is so arched that it does not contribute appreciably to the strength of a contraction? Bompa could certainly be correct given certain characteristics of muscle, which I have to go off and look up now.

Dammit Jim, I’m a physicist not a biologist!
[/quote]

I am interested where you derived these formulas. I’ve been playing arounf with trying to figure out a way to determine absolute strength–as in what you are asking here. I used some data from masters powerlifters and plotted a bodyweight v. weight lifted and noticed a plateuing around the 900# mark on the squat. Meaning as people got more massive strength did not improved much past 900#.

I do not understand how you derived these. I guess I would need to see the “geometry” you are working from. Also, how do you quantize neural strength. I don’t think an equation can be generalized with just geometry. I am interested to see your derivation.

[quote]W.E.C wrote
Dammit Jim, I’m a physicist not a biologist!
[/quote]
What did you do your research in? I’m interested in gravitation–specifically in unifying it with quantum physics.

I just skimmed your post and think I understand what your saying…

It seems to me no matter the arch the muscle will still be applying some force and every little bit helps right?

Also limits of muscle size should keep this from being a problem… expecially for a none drugged trainer

[quote]
It seems to me no matter the arch the muscle will still be applying some force and every little bit helps right?

Definitely true, and the bigger the muscle gets, the more fibres you could pack around the circumference. But if the number of fibres is fixed, then there is a point where the decreased leverage and substrate compressibility will make increasing the size of the fibres detrimental.

Also limits of muscle size should keep this from being a problem… expecially for a none drugged trainer[/quote]

I think you’re right on that one.

In benching there is still an advantage to be gained by getting bigger, simply because the bar has a shorter distance to move. It doesn’t even matter if the extra mass is fat. Check out a video of Gene Rychlak (sp?) benching and you will see what I mean.

I am interested where you derived these formulas.

The formulae are from a straightforward application of pythagorus and the definition of cosine. My description was pretty opaque, I’ve included a diagram that should make it a whole lot more clear.

Neural effects, and the rapidity with which a contraction can be initiated make a huge difference. Indeed this is one place where I think Westide misinterprets Zatsiorsky, but that’s another post…

I’ve been playing arounf with trying to figure out a way to determine absolute strength

Have you ever examined the Wilks formula? It is very similar to what you are doing. He takes a linear regression (I think it’s 3rd order but don’t quote me on that) between totals, and bodyweights of the winners of IPF worlds for the last x years, and then uses that function to determine the coefficients that are applied. What you can see from Wilks is that it flattens out substantially as you get more and more massive: Essentially it says that it is little easier for a 170kg guy to total 1000kg (543W) than it is for a 150kg (552W) guy, but a lot easier than 130kg guy (566W).

I’m a physicist by education, but I work in IT…I’m working on some volunteer stuff, but…

Unification of Gravity with the other three forces or unification of Quantum and General Rel?

[quote]W.E.C wrote:

I’ve been playing arounf with trying to figure out a way to determine absolute strength
[/quote]

I am not a physicist; however, I do understand biology. There are extreme circumstances where adrenalin secretion alone in stressful situations can cause an unbelievable burst of strength that is considered phenomenal. Wouldn’t that alone erase the possibility of “absolute strength” based on muscle contractile proteins alone? You are completely disregarding the mental component…which in my opinion is given far less credit than it deserves.

Professor;

This post was solely about the physical aspect of a single muscular contraction, but your point is well taken. In order to talk about the ability to actually lift a weight I think there are a number of factors that actually play a part:

1. Limit strength of the muscles, with the weakest muscle limiting

2. Relationship between the individual?s ability to generate force and the length of time the lift takes. If the lift takes 0.7 seconds, and the person is well-tuned, requiring ~0.4s to generate max force then the lift will be easy. If the person is not well tuned and needs 0.8s to generate max force, the lift will be hard. This depends on both speed and amount of recruitment.

3. Coordination of the individual. I can?t count the number of benches I?ve missed because I have blown the technique: elbows-flaring, not transitioning to the tris, etc. A well coordinated person can lift more, even thought they may not be stronger.

4. Leverages. Shorter limbs=shorter lever arms, and for the same amount of torque applied by the tricep, a stronger force is applied to the hand.

Basically I see the purely physical aspect of it as setting the upper limit of force you can generate, and the neural/mental aspect sets what percentage of that potential you will be able to use.

Consequently I would have to disagree with adrenaline or extreme excitement allowing strength levels beyond the limits of the muscles. What would be generating the force in this case? I would happily agree that extreme excitement will allow you to access a far greater percentage of the muscular potential (absolute strength).

Have I misunderstood your objection?

[quote]W.E.C wrote:

Have I misunderstood your objection?

[/quote]

I think you have. You have also severely underestimated the human body. For your hypothesis to be correct, everyone who is the same size as someone else in terms of muscle mass and bone structure should share near the exact same level of strength. I have seen a guy who weighed all of 140lbs at 5’10" bench press 315lbs for a max weight.

Take this article for instance where a miner cut off his own arm, but due to adrenaline blocked pain during the procedure.

During extreme stress, adrenaline (epinephrine), noradrenaline and cortisol are released into the blood stream, shunting blood away from internal organs to muscle tissue. This is the fight or flight response. Many of the phenomena involved are not completely understood as some cases defy direct scientific explanation outside of what I listed above.

While you focus only on the physical and try to relate all strength to only units of power over a given amount of muscle proteins as related to limbs and levers, you ignore what many still consider amazing that defies this alone.

In order to create a defined “absolute strength”, all strength would be without the ability to super-conduct force during times of extreme stress.

The answer to this is largely unknown in extreme cases. If it was completely understood, you would have your explanation of absolute strength. The point I am making is that everything about what our bodies are capable of has not been completely understood up to this point. Many of the processes considered fact are still largely hypothesis.

[quote]Professor X wrote:
W.E.C wrote:

Have I misunderstood your objection?

I think you have. You have also severely underestimated the human body. For your hypothesis to be correct, everyone who is the same size as someone else in terms of muscle mass and bone structure should share near the exact same level of strength. I have seen a guy who weighed all of 140lbs at 5’10" bench press 315lbs for a max weight.

Take this article for instance where a miner cut off his own arm, but due to adrenaline blocked pain during the procedure.

During extreme stress, adrenaline (epinephrine), noradrenaline and cortisol are released into the blood stream, shunting blood away from internal organs to muscle tissue. This is the fight or flight response. Many of the phenomena involved are not completely understood as some cases defy direct scientific explanation outside of what I listed above.

While you focus only on the physical and try to relate all strength to only units of power over a given amount of muscle proteins as related to limbs and levers, you ignore what many still consider amazing that defies this alone.

In order to create a defined “absolute strength”, all strength would be without the ability to super-conduct force during times of extreme stress.

Consequently I would have to disagree with adrenaline or extreme excitement allowing strength levels beyond the limits of the muscles. What would be generating the force in this case?
The answer to this is largely unknown in extreme cases. If it was completely understood, you would have your explanation of absolute strength. The point I am making is that everything about what our bodies are capable of has not been completely understood up to this point. Many of the processes considered fact are still largely hypothesis.
[/quote]

Very true. The human body is a machine that transcends physical analysis; to try to reduce it to mere physical equations would be a gross underestimate. There various theories on how the human body functions, be it Chinese medicine, Ayurvedic medicine, Western medicine, etc., all the fruit of man’s effort to understand the world’s most complex machine. No one system contains every truth, Chinese doctors can fix a lot of problems Western doctors can’t, and some problems can be solved by one system of medicine that another cannot. However, no effective and time-tested system of medicine reduces it to physics equations. The human body is a fascinating machine that has stood the test of time, and can adapt to almost any stimulus; to reduce it to an equation of physics would be ridiculous.

When I was in college, I wasted many hours of precious drinking time thinking of shit like this. Now I just lift.

[quote]KombatAthlete wrote:
The human body is a fascinating machine that has stood the test of time, and can adapt to almost any stimulus; to reduce it to an equation of physics would be ridiculous.[/quote]

Yeah, it would definitely take more than one equation, and a hell of a lot of anatomical knowledge. Other than that, no problem other than getting all the data to drive the exercise. This is called biophysics.

As a practical matter, yes there is a limit to how much stronger hypertrophy can make you. You’re limited by the tensile strength of your connective tissue. Folks who use 'roids often run painfully into this limitation.

Also as a practical matter, training for maximum strength is pretty different from training for maximum hypertrophy.

I’m a student massage therapist, specializing in treatment and sports massage along with learning fitness training. It seems to me that as the muscle contracts it firms up, the outer muscle fibers would use the arc as a pully type system. This seems to make the most sense to me thinking back to the end of a contraction is usually the strongest. I’ll ask me kinesiology instructor on Monday.