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Muscles

I've been reading Bud Charniga’s translations and it is apparent that the Russian weightlifting coaches and sports scientists were very knowledgeable on all aspects of physiology so I feel it is necessary to be similarly knowledgeable...

Before the advent of the electron microscope nobody really knew how muscles contracted. I have the 20^th edition of Gray's Anatomy published in 1918 (I prefer it to the modern atlases) that proposes that muscles swell up with a gel like plasm in a similar manner to the way it was thought that amoeba move.

It is now known that contraction is caused by the action of myosin (purple) filament heads pulling ratchet like on actin (pink) filaments. This is called the Sliding Filament Theory, though everyone accepts it as fact.

The basic contractile unit of a muscle fibre (cell) is the sarcomere which extends from the one Z line to the next. Note that the actin filaments are longer than the myosin filaments. With the above diagram the filaments are at full extension so virtually no *contractile* force is developed - however owing to the elasticity of the connective tissues which encase the muscle fibres the muscle as a whole generates a degree of *passive* force.

At this point maximum contractile force is being developed because the maximum number of myosin heads are connected. No elastic force is generated.

At this point no external force is being generated, the Z lines are jammed into the ends of the myosin filaments and the actin fibres have squeezed past one another and blocked off some of the myosin heads.

The filaments in voluntary muscle line up across the entire muscle fibre producing a striped appearance (visible in a light microscope). In cardiac muscle the lining up is less distinct and in smooth muscle there is no lining up.

Fibre Type

Muscle fibres are generally divided into 2 types, fast and slow twitch. The difference between these 2 types is that they develop the same forces but at different speeds:

FAST FIBRE		SLOW FIBRE

10 ms cycle = 1 ms pull + 9 ms recovery		25 ms cycle = 1 ms pull + 24 ms recovery

	fastest			strongest			fastest			strongest

dist	force	time	dist	force	time	dist	force	time	dist	force	time
nm	h	ms	nm	h	ms	nm	h	ms	nm	h	ms

15	1	1	15	1	1	15	1	1	15	1	1
30	1	2	30	2	11	30	1	2	30	2	26
45	1	3	45	3	21	45	1	3	45	3	51
60	1	4	60	4	31	60	1	4	60	4	76
75	1	5	75	5	41	75	1	5	75	5	101
90	1	6	90	6	51	90	1	6	90	6	126
105	1	7	105	7	61	105	1	7	105	7	151
120	1	8	120	8	71	120	1	8	120	8	176
135	1	9	135	9	81	135	1	9	135	9	201
150	1	10	150	10	91	150	1	10	150	10	226
165	2	11	165	11	101	165	1	11	165	11	251
180	2	12	180	12	111	180	1	12	180	12	276
195	2	13	195	13	121	195	1	13	195	13	301
210	2	14	210	14	131	210	1	14	210	14	326
225	2	15	225	15	141	225	1	15	225	15	351
240	2	16	240	16	151	240	1	16	240	16	376
255	2	17	255	17	161	255	1	17	255	17	401
270	2	18	270	18	171	270	1	18	270	18	426
285	2	19	285	19	181	285	1	19	285	19	451
300	2	20	300	20	191	300	1	20	300	20	476
315	3	21	315	21	201	315	1	21	315	21	501
330	3	22	330	22	211	330	1	22	330	22	526
345	3	23	345	23	221	345	1	23	345	23	551
360	3	24	360	24	231	360	1	24	360	24	576
375	3	25	375	25	241	375	1	25	375	25	601
390	3	26	390	26	251	390	2	26	390	26	626
405	3	27	405	27	261	405	2	27	405	27	651
420	3	28	420	28	271	420	2	28	420	28	676
435	3	29	435	29	281	435	2	29	435	29	701
450	3	30	450	30	291	450	2	30	450	30	726
465	4	31	465	31	301	465	2	31	465	31	751
480	4	32	480	32	311	480	2	32	480	32	776
495	4	33	495	33	321	495	2	33	495	33	801
510	4	34	510	34	331	510	2	34	510	34	826
525	4	35	525	35	341	525	2	35	525	35	851
540	4	36	540	36	351	540	2	36	540	36	876
555	4	37	555	37	361	555	2	37	555	37	901
570	4	38	570	38	371	570	2	38	570	38	926
585	4	39	585	39	381	585	2	39	585	39	951
600	4	40	600	40	391	600	2	40	600	40	976
615	5	41	615	41	401	615	2	41	615	41	1001
630	5	42	630	42	411	630	2	42	630	42	1026
645	5	43	645	43	421	645	2	43	645	43	1051
660	5	44	660	44	431	660	2	44	660	44	1076
675	5	45	675	45	441	675	2	45	675	45	1101
690	5	46	690	46	451	690	2	46	690	46	1126
705	5	47	705	47	461	705	2	47	705	47	1151
720	5	48	720	48	471	720	2	48	720	48	1176
735	5	49	735	49	481	735	2	49	735	49	1201
750	5	50	750	50	491	750	2	50	750	50	1226

The figures in the above table represent a simple model of an myosin and actin filament. The heads on the myosin filament and the attachment sites on the actin filament are each taken to be 15 nm apart and each take up 750 nm lengths on their respective filaments.

Regardless of whether the fibre (or more accurately filament) is slow or fast the contraction time of the myosin head is taken to be 1 ms. However the recovery time of the fast fibre is taken to be 9 ms and the that of the slow fibre to be 24 ms. Thus the fast fibre has a cycle time 2.5 times faster than the slow fibre (and so uses up energy at 2.5 times the rate).

Both fibres are taken to be fresh at the start rather than repeatedly contracting.

The force and time columns are of the most interest. For example a myosin filament can engage only one myosin head (force h = 1) when pulling the actin filament over the first 15 nm, it does this in 1 ms.

However in the fast fibre after 10 ms (150 nm) a second head can operate because the first head has had 9 ms to recover. But with a slow fibre it takes 25 ms (375 nm) before a second head can be engaged. The result overall is that both fast and slow fibres contract at the same maximum speed but the fast fibre generates more force.

Similarly both fibres can generate the same max force at any point in the contraction but it takes longer for the slow fibre to get there.

The result in practical terms is that fast fibres move against particular forces faster than slow fibres.

Note that although it seems like each head of the myosin filament is under individual control that this is not the case. All the head does is respond to whether the actin binding site is close to it and it only does this in the presence of the energy molecule ATP which is utilised when calcium ions are released in response to neural impulses.

Thus a single muscle fibre doesn't respond in an all or none way. The magnitude and frequency of neural impulses determines how much ATP is available to the actin-myosin binding sites and how many fibres are stimulated.

Whenever a muscle fibre contracts a chemical reaction at the binding site (blue) on the actin molecule takes place. A myosin filament is actually composed of numerous myosin 'hockey sticks'. In the presence of calcium ions (Ca⁺⁺) the binding site is exposed so that head of the stick attaches to it. The head then flexes powered by the energy from ATP.

The left side of the above diagrams show the myosin hockey stick from the side, whilst the right side shows the hockey stick and actin molecules in transverse section.
TM - tropomyosin
T - Troponin T, high affinity for TM
C - Troponin C, calcium binder
I - Troponin I, inhibits actin-myosin ATPase

From the table it can be seen that this reaction happens many times per second (40-100 Hz), the result being that flexing of the myosin head pulls the actin filament along somewhat like a man climbing a rope.

Muscle Model

The strength curve of a muscle is derived from an active component (the myosin and actin filaments) and a passive component (the elasticity and shock absorption of the connective tissues).

Muscles are thus modelled on a glut of springs, dampers and contractile components. For simplicity I have considered a single contractile component (the purple myosin and pink actin filament), a single parallel elastic component (the black spring) all enclosed in a fluid filled damper (the red muscle bag).

The spring's resting length depends on the type of muscle, for discussions sake I will define it as occuring when the sarcomere's length is 2.11 µm. Thus when totally relaxed the muscle's length (and therefore joint position) settles at 2.11 µm.

You can see this by letting your arms float in a swimming pool - the elbow joint ends up roughly at right angles, however this is determined by the relaxed tension of a number of flexors and extensors and the position of the shoulder joint. If the triceps were to be cut then the elbow would settle into a more flexed position.

At this point the muscle is at its longest whilst still being able to develop active contractile force. It could be stretched further but the contractile force would be passive, i.e. no different than a 'dead' muscle.

Maximum contractile force is being developed there being maximum myosin-actin connection. The spring is at its resting length.

The sarcomere is contracting against itself. The spring is pushing out.

Strength Curve

The strength curve of the sarcomere is determined by plotting the tension curve of the actin-myosin filament and the elastic tension of the associated connective tissues. These forces are added together to get the total tension.

In practice the total strength curve of a muscle is measured by simply stretching it and measuring the force it produces as it elongates. The same method is then used but whilst the muscle is activated. Thus the total tension minus the elastic tension gives the active tension of the whole muscle. With sensitive instruments this can be done for a single muscle fibre. The actual length-tension curve of a whole muscle is smooth thus justifying the name curve.

Length-tension curve for a single sarcomere
active tension (red line) + elastic tension (blue line) = total tension (green line)
It should be noted that the sarcomere model is artificial in that it assumes that the spring tension is like that of a metal spring.

The above model shows the length-tension curve of an isometrically contracting sarcomere. Thus the sarcomere is set at a certain length and the tension at that length is measured - it is assumed at each length that the actively contracting sarcomere is fully refreshed.

Cheating and the Strength Curve

The term 'cheat' implies that one is trying to get something for nothing.... however in this article it is treated as a strictly biomechanical term.

Earlier I described how the mechanics of the individual sarcomeres give a smooth muscle curve such as:

This curve would be derived from a series of isometric measurements, thus minimising errors due to fatigue and friction.... for example fatigue even during a single concentric rep would distort the curve so that it would look weaker at shorter lengths. One would also have to take into account that a muscle measured in vivo would be different to that in vitro.

A barbell provides up and down resistance. The magnitude of this resistance can be calculated from Newton's formula;

F = m(g+a) (see Force)

F - force (Newtons (N) (kg.m.s^-2))

m - mass (kg)

g - gravitational acceleration (10 m.s^-2)

a - acceleration (m.s^-2)

Thus the 'weight' of a barbell is determined by gravitation and the acceleration applied to it.

Thus the weight of a barbell can be altered by varying the acceleration applied to it, where;

a = F/m - g

Example

Imagine a Preacher Curl where the biceps muscle produces a constant force of 6000 N. The barbell moves at a constant vertical velocity....

Constant Force

Given the dimensions shown in the diagram a muscle producing 6000 N of force would require a 100 kg barbell mass moving at constant velocity (g = 10 m.s^-1).

However a muscle does not have a flat strength curve. Assume for simplicity that it ramps up in linear fashion as it contracts....

Increasing Force

Take a 120 kg barbell. This would be too heavy to curl strictly, but if given an initial velocity the bar can decelerate and thus feel lighter so that the muscle force must be 6000, 7000 then 8000 Newtons in the diagrams.

Alternately assume that the muscle's force decreases as it contracts....

Decreasing Force

Here the figures are reversed so that the bar starts with a positive acceleration but has a deceleration at the top so that the muscle force goes from 8000 to 6000 Newtons.

Compensatory Deceleration

Fred Hatfield often talks about compensatory acceleration. For example one would lower into a Squat and on ascending they would apply maximum force to get past the sticking point, once past the sticking point the weight would feel lighter but one would compensate by accelerating to make it feel heavier.

However I prefer (where possible) to apply compensatory deceleration. This has 2 benefits;

More weight can be lowered.
If the correct weight is chosen the point of zero acceleration can be made to coincide with the point of minimum (sometimes zero) velocity and thus a maximal weight can be handled at the muscle's strongest point of contraction.

Thus cheating allows one to vary the force applied to a muscle both on the positive and negative strokes of a lift. Also by making the weight travel slowest at its strongest point it also generates the greatest stimulus.

The problem with compensatory acceleration is that the weight moves fastest at the point where the muscle is strongest. A muscle which is contracting quicker trades off some of the force that it can generate (the force-velocity curve). One is also somewhat fatigued by the time one gets to this point (having had to struggle slowly through the sticking point) so the actual amount of force generated is not nearly as great as if one were to do say a partial from this point. This is why one can lockout a huge weight but have trouble locking out a full move. In a sense cheating is a way of getting the best bits of full and partial moves and putting them into one lift.

6^th October 2023