Relationship between muscle length and tension

This chapter is most relevant to Section L1(iv) from the 2017 CICM Primary Syllabus, which expects the exam candidates to "describe the relationship between muscle length and tension". The exam-oriented learner would be correct to dismiss this topic from the list of their last-minute cramming, as its contribution to the past papers has been modest to say the least. Question 3 from the second paper of 2019 was the only time this was asked, and it was only 50% of a question that otherwise seemed to be asking about the Frank-Starling mechanism.

The paper by Nishikawa et al (2018) is an excellent overview of muscle mechanics, but probably brings in all sorts of irrelevant elements (eg. force-velocity relationships and history dependence are probably not essential reading here), and the time-poor exam candiate is advised to restrain themselves from reading beyond the "force-length relationship" section.  If one were so inclined, one may pay Springer for the privilege of reading this chapter by Herzog et al from Muscle Biophysics (2010), which was extremely helpful in writing this chapter.

Definition of the length-tension relationship

Length-tension relationship of muscle would probably need to be defined for a written exam answer, and one might think that one could have no source more authoritative than the Encyclopedia of Neuroscience:

"The length-tension property of a whole muscle (or muscle fiber or sarcomere) is the relationship between muscle length and the force the muscle can produce at that length."

In a way this definition may seem to confuse things by using the term "force". Most times length-tension relationships are discussed in terms of tension because the muscle can be regarded as a rope, in the sense that it pulls but can't push. Other authors do tend to bring force into the definition, and in fact "force-length relationship" is a search string that seems to yield a better quality of definition, such as this one (from the same source):

"The force-length relationship describes the dependence of the steady-state isometric force of a muscle (or fiber, or sarcomere) as a function of muscle (fiber, sarcomere) length. It is characterized by a positive slope (i.e. force is getting greater as length increases) at short lengths (the so-called ascending limb of the force-length relationship), a zero slope (the so-called plateau region) at intermediate lengths, and a negative slope (i.e. force decreases with increasing lengths; descending limb of the force-length relationship) at long muscle lengths."

This is accurate and comprehensive, but too verbose for the last-minute cram panic of the CICM exam candidate. The official college answer to Question 3 from the second paper of 2019 does itself make some attempt at a much shorter definition: 

"there is a resting length at which tension developed on stimulation is maximal"

But that leaves us without an explanation of what "resting length" is, and in fact the  unlucky reader who has found their way into the dense thicket of muscle biophysics literature will soon discover an embarassing confusion of length terminology which probably needs to be managed here somehow. There's resting length, slack length, optimal length, and so on. You'd think some professional body or authoritative textbook would bring these together into a table of standard definitions, but you'd be wrong - the best resource appears to be this paper by Fridén & Lieber (1998), discovered via this excellent blog post by Andrew Vigotsky:

• Optimal length – Length at which myofilament overlap is optimal and force is maximal (2.6-2.8 µm in human muscle, 2.0-2.2 µm in frog muscle)
• Slack length – Length at which muscle force equals zero; this length is unknown for most human muscles but is the retracted length that a muscle becomes after the tendinous insertion is cut
• Resting length – A clear definition of this length is not possible, since passive tension is variable between muscles and the resting condition is not well defined; should not be used to describe an absolute length
• In situ length – Muscle length under a specified joint angle configuration; should not be used to describe an absolute length
• In vivo length – Muscle length under a specified joint angle configuration; should not be used to describe an absolute length

There is no possible way that any ICU trainee would ever be expected to know this level of detail, or to be able to coherently debate the value of the potentially pointless term "resting length" with a tired examiner during a cross-table viva; and so some kind of short pithy definition is required that might sacrifice accuracy in return for brevity. The reader is left with this homegrown option, while the suggestion box waits for a better one:

The tension generated by a sarcomere depends on the length of the sarcomere, and there is an optimal length at which tension is maximal, which in humans is ~2.7 µm.

It is probably better to refer to sarcomeres than it would be to discuss whole muscle,. Whole muscles are a fairly heterogeneus group and what one says about the biceps may not necessarily apply to the diaphragm; moreover when whole muscles are tested all sorts of extra complexities are introduced (for example, the progressive dispersion of numerous different sarcomere lengths gives rise to "creep" phenomena where tension increases over time).  On the other hand, sarcomeres everywhere behave similarly when it comes to length and tension, even as their lengths and tensions may differ- as the underlying physiological mechanism is the same. Which brings us to:

Mechanism of the length-tension relationship in muscle

Most people who write about the physiological basis of the relationship between sarcomere length and isometric tension tend to reference the classic paper by Gordon Huxley and Julian (1966), who seem to be credited with bringing this concept to light. To summarise their findings, these investigators were able to demonstrate that the tension generated was proportional to the degree of overlap between thick and thin filaments. Specifically, they were able to find a "plateau" along the force-length curve which corresponded to the expected length of the bare "H" zone of the sarcomere, where there is no actin and no cross-bridges. Huxley (1963) had earlier measured the contractile elements in the same tissue (frog muscle), producing a thick filament length of 1.6 μm and a thin filament length of  2.05 μm, with a region of around 0.15-0.2 μm which had only thick myosin filaments but no actin. Thus, there is a length of a sarcomere at which there is maximal overlap between actin and myosin filaments, and the overlap is maintained until the myosin starts to slide off the end of the actin. As overlap decreases, the magnitude of the exerted force decreases in proportion to the number of cross-bridge sites lost, until the actin and myosin are completely separated and the force being generated is reduced to zero. 

So, when the college examiners mention that "some candidates utilised a diagram effectively to convey understanding", this is probably some minimum version thereof. However it would probably only score partial marks. To look at it would make the reader think that, with enough stretch, one could simply force the sarcomeres apart, turning the muscle fibre into a yielding mass of disconnected protein that stretches infinitely like melted cheese. Obviously that'ts not what happens. Therefore, to truly impress the examiners, the diagram would also need to include some reference to passive tension and total active tension.

Active tension and passive tension

"Active tension", the concept discussed above, is the tension generated by the sliding actin and myosin filaments which has this logical hump-shaped length-tension relationship. However, this relationship only looks this smooth in an isolated sarcomere on a petri dish, and is is not really representative of how an adult quadriceps is going to perform. Muscle is not only made up of gelatinous sarcomeres - it is also full of tough fibrous connective tissue, and this buttress of unwilling protein is going to resist a stretching force. The term "passive tension" refers to this resistance.

Passive tension develops late in the stretching process, i.e. it plays minimal role in the behaviour of unstressed muscle in the middle of their range of motion. They are simply not pulled upon enough to engage those protein fibres. Only in extreme positions do we see it coming into play, eg. where one is doing the splits, or somehow otherwise extending their muscles to the limits of their range of motion in a way that an unfit forty-something dad cringes to contemplate. This tension resists further stretch, and the degree of resistance increases with increasing stretch just as the sarcomeres are giving up and sliding off each other. This contribution to the total tension of the muscle can be plotted on the same graph, as follows:

Obviously the real world data will violate this lovely smooth relationship with messy data points and confidence intervals; moreover as the connoisseur of steak will note, muscles will vary in their connective tissue content quite considerably, which will influence the magnitude and character of the passive contribution. To illustrate, here are some graphed active and passive length-tension relationships from feline diagastric and thyroarytenoid muscle, from Johns et al (2004):

What specifically in the muscle is contributing to this? Turns out, titin. Whole muscle retained a huge amount of passive tension capacity even after tendinotomy. A series of ingenious experiments carried out in the course of a publically available PhD thesis by Taylor Winters (2012) determined that titin content was the most important contributor to passive tension, and that the collagen and elastin of the endomysium (or the tendons of the muscle, for that matter) contributed minimally.

A discussion of the distinction between active tension and "resting tension" is also mentioned in the CICM examiner comments to Question 3 from the second paper of 2019 as something that would attract "additional credit", as if implying that it would be possible to score more than 10 out of 10 marks by demonstrating this knowledge. What is this concept, and is it different from passive tension? Reading some papers, one comes to realise that "resting tension" and "passive tension" are often confused even in professional literature, and occasionally you might even see them used interchangeably within the same article. This indisciminate use of terminology is seen most frequently in older works, and refers to the tension observed in "resting" (i.e. paralysed or denervated) muscle fibres, eg. where Hill measured "filamentary resting tension (FRT)" from frog sartorius myofibrils in 1968. Looking at that paper, what he was measuring is clearly the thing that would these days be referred to as "passive tension".  Is there really a difference between these concepts? Perhaps for some. It appears that occasionally "resting tension" is used to refer to the "biotensegrity" of tissues, i.e. the combination of muscle tone and connective tissue resistance that contributes to the efficient function of whole musculoskeletal systems (such as, for example, the maintenance of upright posture, which would not be economically viable without tough stretched tendons stiffening the joints). Or, to borrow a turn of phrase from Masi & Hannon (2008), 

"Nature is frugal and Man’s adaptations to gravitational forces and erect postures seemingly evolved mechanisms in skeletal muscle tissues to economically enhance stability",

and of those mechanisms "resting tension" is one, the other being a centrally coordinated co-contraction of muscles on either side of posture-critical joints. That second mechanism is surely dominant, because a person who loses central motor control tends to collapse in a heap; whereas if "resting tension" was the most important component, an unconscious person would remain upright like a toy soldier, kept stable by the resting tension of their muscle.

What is the point of this digression?  Reader, if there is any distinction between the concept of resting tension and passive tension, it must surely be meaningless for the CICM candidate, as the examiners won't be distracted by this sort of trivia, being much more interested in the implications of the length-tension relationship for cardiac muscle. And so,

Length-tension relationship in cardiac muscle

Most people would be more familiar with this concept as "the Frank-Starling relationship", but the two concepts are sufficiently distinct to be considered separately in two separate chapters. For those unwilling to dredge through pages of Deranged Physiology wank, Allen & Kentish (1985) describe the molecular mechanisms of this relationship very well, and their explanations remain valid even though the paper is older than most of the current First Part examiners. To summarise:

• The relationship between preload and contractility is a relationship between length and tension, because:
  • Preload results in an increased sarcomere length
  • As preload increases, contractility (tension generated by the cardiac myocytes) increases

There is even an "optimal length" for the myocyte sarcomeres, which is also about 2.2 μm according to some early light microscopy studies by Gay & Johnson (1967). However, apart from this, the length-tension relationship graph for cardiac myocytes looks a lot different to the one for normal skeletal muscle. The most important feature is that for skeletal muscle, at optimal length, there is barely any passive tension contribution; whereas in cardiac myocytes it contributes 50-80% to the total tension.

These values and concepts, reproduced in countless papers and textbooks, come from a rare old paper by Spiro & Sonnenblick (1964), rare because nobody seems to have those back issues of Circulation Research from the sixties. Below, the original diagram by these authors (from experiments on the frog sartorius and a cat papillary muscle) has been vandalised to include elements that the CICM trainee should reproduce in their exam paper:

In textbooks, and therefore in the minds of the examiners, these classical tracings are usually combined into one graph, and percentages of length and tension are typically overlaid to demonstrate the most important features:

• Skeletal muscle has a wider range of lengths over which its tension is near-optimum. At about 75% of the optimal length, skeletal muscle tension is close to maximum already, whereas for cardiac muscle the active tension is zero at that length.
• The cardiac myocyte length-tension relationship is steeper (increasing cardiac myocyte length from 75% to 90% of the optimal length increases the active tension from 0 to 70% of the maximum)

Of the diagrams that represent this, the best is probably from Sequeira & van der Velden (2015) - reinterpreted (oversimplified) here:

Candidates who utilise this diagram effectively to convey understanding should also aim to make mention of the fact that these diagrams are usually derived from studies of little strands of papillary muscle, and that a whole heart is a much tougher and more fibrous structure, which will behave very differently. The more practical way to understand the relationship of whole-heart myocardial stretch to the generation of force is to look at ventricular pressure-volume loops, which is a whole separate topic of its own.

Smooth muscle length-tension relationship

All this talk of optimal sarcomere length completely sidelines smooth muscle, as this tissue has no sarcomeres, but still does have a length-tension relationship. This has never appeared in CICM past papers, and in any case whether this relationship is worth discussing or not scarcely depends on which side of an exam you find yourself on, as approximately 100% of the people on the wrong side will scoff at the irrelevance of what follows, and so will 99% of those who have already passed. For the rest, the best reference is this ancient paper by Gordon & Siegman (1971).

To summarise that work so that no exam candidate is tempted to read it, you don't need sarcomeres to have a length-tension relationship. Smooth muscle may have no orderly rows of contractile proteins, but there are still actin and myosin filaments sliding against each other, which means there must be some length at which some maximum contact between these proteins occurs; and similarly there must be some length at which contact no longer occurs. And just like skeletal and cardiac muscle, smooth muscle has connective tissue and titin strands that create passive tension at the upper limits of stretch. The problem with describing these is that smooth muscle arrangements are massively heterogeneous, with some tissues capable of contracting in response to stretch, others relaxing, and yet others dancing to the beat of their own pacemaker. What's true for the uterus will not be true for the iris or the anus. Taking the point of view that vascular smooth muscle is the type an intensive care trainee (and exam question writer) would have the greatest interest in, here is a nice representative plot of passive and active tension vs. length from the porcine carotid by Herlihy & Murphy (1973):