The cellular basis of the length-tension relation in cardiac muscle.
The Frank–Starling law of the heart represents the relationship between stroke volume and end In contrast, the relaxed sarcomere length of cardiac muscle cells, in a resting ventricle, is lower than the optimal length for contraction. understanding of the relationship between active tension and sarcomere length, Starling. The cellular basis of the length-tension relation in cardiac muscle. for a large part of the rapid change in developed tension when muscle length is altered. The steepness of the cardiac length-tension relation arises because the degree part of the rapid change in developed tension when muscle length is altered.
This relationship is altered by changes in both preload and inotropy. The former shares some similarities with skeletal muscle; the latter, however, is unique to cardiac muscle.
How Preload Affects the Force-Velocity Relationship If preload is increased, cardiac muscle fibers will have a greater velocity of shortening at a given afterload see figure.
Conversely, if preload decreases, the velocity of shortening decreases at a given afterload.
This occurs because the length-tension relationship dictates that as the preload is increased, there is an increase in active tension development. Once the fiber begins to shorten, the increased tension generating capability at the increased preload results in a greater velocity of shortening. In other words, increasing the preload enables to muscle to contract faster against a given afterload.
In skeletal muscle this relationship between sarcomere length and tension has been firmly established, and its functional significance is generally agreed. The behaviour of sarcomeres in cardiac muscle has been investigated much less thoroughly; under physiological conditions they appear to operate in the length range from about l. However, relatively few observations have been made on the relationship between sarcomere length and developed tension in cardiac muscle, and these are to some extent conflicting.
This may be because of technical problems, particularly those of tissue distortion during histo logical preparation; methods have recently been developed to measure sarcomere length in vivo, and these may resolve the question. At present, it seems well established that no active tension is developed at sarcomere lengths less than about 1. In between it is not clear whether increasing tension is the result of successive increments in sarcomere length as in skeletal muscle, or recruitment of increasing numbers of sarcomeres in muscle-fibres which were buckled at short muscle-lengths and are straightened and then stretched as the muscle lengthens.
Furthermore, there is recent evidence that the curve relating tension and sarcomere length Fig. We need a more detailed knowledge of the behaviour of actin-myosin cross-linkages to settle these uncertainties.
In skeletal muscle, the linear relationship between muscle-length and sarcomere length is maintained until the latter reaches at least 3. For heart muscle, the situation at high degrees of stretch is different. Sarcomeres will lengthen to only about 2. This situation does not arise in the normal heart and seems very unlikely even in the failing or pathological heart; in acute experiments where the relaxed left ventricle was distended with pressures as high as mm Hg far in excess of the levels reached even in severe heart disease the sarcomeres in the ventricular wall had an average length of only 2.
Dynamic mechanical properties of cardiac muscle. The length-tension curve describes an important property of muscle under static conditions - held at a constant length both before and during activity - but it throws no light on the dynamics of muscular contraction, which are of fundamental importance to any understanding of heart muscle performance. A stimulated muscle goes through a period of mechanical activity the 'active state' which reflects the release of energy derived from chemical reactions and has measurable properties both of duration and intensity.
Enormous progress has been made in elucidating and measuring both the biochemical steps which yield energy, and the mechanical behaviour which is the expression of this energy release. The literature is voluminous, reflecting both the technical difficulties involved in research on the myocardium and its innate complexity, and the subject can only be briefly surveyed here.
The commonest material used for experimental study of the mechanical properties of heart muscle has been papillary muscle, removed from the right ventricles of young animals under anaesthesia. It can be obtained in this way as extremely thin strips a few millimetres in length, and made up of numbers of fairly parallel muscle fibres. When such papillary muscles are mounted in oxygenated, nutrient media of appropriate ionic and osmotic properties, they preserve their contractile properties in response to electrical stimulation for long periods.
These contractile properties have been interpreted largely in terms of very simple mechanical models; to demonstrate why such models were chosen it is necessary briefly to describe some early experimental work carried out on skeletal muscle.
Intact skeletal muscles can be removed easily from small animals such as the frog, and a number of workers in the early years of the twentieth century studied these muscles, stimulating them electrically and examining the mechanical properties and heat production during contraction the latter phenomenon having been demonstrated by Helmholtz over fifty years previously.
As was mentioned earlier, electrical stimulation of muscle leads to tension development. In the resting state, a potential difference of about 90 mV is maintained across the membrane of the muscle-cell - the resting potential.
An externally applied shock can cause transient reversal of polarity of this potential, followed by slow recovery. This discharge, which is known as the action potential, triggers the release of calcium ions from stores within the muscle-cell, and these somehow activate the cross-linkages between the actin and myosin rods in the contractile apparatus of the sarcomeres. This whole process occurs within milliseconds, and the muscle cell is then capable of contracting i.
Thus a single electrical stimulus applied to a muscle-fibre causes a short-lived contraction appropriately known as a twitch. A chain of stimuli causes repetitive twitches, and in skeletal muscle if the stimulation frequency is high enough the twitches will fuse together to give a sustained contraction.
This is known as a tetanus, and the corresponding train of shocks is a tetanic stimulus. For a given muscle preparation, the tension generated in each twitch or tetanus will increase with increasing stimulus strength until a maximum is reached which is highly reproducible over long periods of time. If the muscle is held at constant length, the twitch or tetanus is known as isometric; if it is allowed to shorten, the force if any opposing shortening is described as the load or afterload and if this force is constant, which implies that all accelerations of the load are very small compared to that due to gravity, the contraction is called isotonic.
Since maximal isometric contractions were found to be highly reproducible, they were used experimentally as the baseline condition; in this case the muscle generated heat during the course of a stimulation cycle, but since no shortening occurred, no external work was done work, or energy, is equivalent to force times distance.
- Length-tension relationship
- Cardiac Muscle Force-Velocity Relationship
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When muscles were allowed to shorten by a distance x against a load or force P, not only were Px units of work done, but an extra amount of heat was released.
This effect of shortening on heat production is known as the 'Fenn effect' after its discoverer; Fenn an American physiologist who did this work in also demonstrated the converse to be true - if a muscle was stretched during stimulation, it gave out less heat than when held at constant length.
In describing this experiment, Fenn coined a phrase, 'negative work', which has given pain to physical scientists ever since; this is unfortunate, since the implication of the experiment - that the mechanical conditions during contraction control the amount of energy released - is fascinating and appears to have been little explored.
The explanation of this liberation of excess heat on shortening came some years later when instruments capable of following heat-production instant by instant through the contraction and relaxation cycle became available.
It was then shown in a famous series of experiments carried out by A. Hill that the extra heat associated with shortening is proportional to the distance x shortened; thus it is equivalent to ax units of work where the constant a has the dimensions of force. This rate of energy liberation was found experimentally to increase as load diminished, having its highest value when the load was zero and being zero when the muscle exerted its maximum force in an isometric contraction.
Thus the properties predicted from thermal measurements were open to confirmation by purely mechanical experiments, and were indeed verified when the velocity with which a muscle could shorten isotonically against various loads was examined Fig. Relationship between load P grams-weight and velocity of shortening v cm s-1 in isotonic shortening of frog skeletal muscle.
The points were obtained experimentally; the line was derived from Equation The thermal observations were, however, of great importance in another way, since they suggested the first conceptual mechanical model of the muscle fibre.
Observations on the course of heat release in the very early stages of stimulation revealed that it was similar for both isometric and isotonic contractions. This suggested that similar mechanical events were occurring in the early stages of both types of contraction, and since the length of the muscle fibre could not change in an isometric contraction, the idea arose of a contractile element in the muscle, which shortened on stimulation but which was linked in series to an elastic element that could lengthen if muscle length was held constant Fig.
Mechanical models of muscle. The force-velocity relationship described above was assumed to describe the properties of the contractile element, since in steady shortening under isotonic conditions the elastic element would have constant length and would not contribute.
It should be stressed that Hill was examining the properties of skeletal muscle under very particular conditions. First, the muscle was stimulated with trains of high frequency shocks tetaniso that a prolonged and maximal response occurred.
Thus each observation was carried out with a constant load and a steady velocity of shortening. The real physical properties of the series elastic element were not considered, since it was at constant length throughout. Similarly, the time-course of development or decay of force was ignored.
Furthermore, resting tension was very small at the muscle-lengths used approximately 2 per cent of active tensionand therefore a model with two elements was adequate. The addition of a component to account for tension in the resting state parallel elastic component, as in Fig.
Finally, the exact nature and location of the contractile element and the series elastic element also remained undefined; structures such as tendons might represent a genuine elastic element, or the internal contractile mechanisms might be elastic. Nonetheless, this 'two-element' model of active skeletal muscle achieved widespread acceptance, since it explained a range of mechanical and thermal observations. It was natural, in view of the structural similarity which exists between sarcomeres in cardiac and skeletal muscle, to consider its applicability also to cardiac muscle.
First, cardiac muscle preparations exhibit appreciable tension throughout the range of lengths from which they will contract; thus the parallel elastic element becomes an essential part of the model, and the force-velocity relation can be examined only incompletely, since forces at and near zero cannot be achieved.
Second, and far more important, is the fact that under normal conditions it is not possible to tetanize cardiac muscle like skeletal muscle and get a sustained and highly reproducible isometric contraction. Cardiac muscle repolarizes relatively slowly, and repeated stimuli do not produce a steady, maintained contraction.
Instead, they produce twitches which even at high stimulation frequency only partially merge, giving a 'saw tooth' time-course of tension or shortening. Thus an incomplete cycle of relaxation and contraction occurs with each stimulus. At lower frequencies, stimuli evoke twitches which are clearly separated and may be highly reproducible, but neither of these types of response represents a steady state of activity, since the tension-generating and shortening capacity of the muscle its active state may be changing continuously during a contraction.
A series of twitch responses from a papillary muscle preparation is shown in Fig. A series of superimposed records showing the length and tension changes that occur in a cat papillary muscle which contracts against a series of different loads.
The initial length was held constant; the lower family of curves shows that tension rose to match the load in each case, and then remained constant whilst shortening occurred. The amount of shortening at each load is shown in the upper curve. The final tension curve shows the response when the muscle cannot lift the load; this is the isometric twitch response. This greatly complicates the design and interpretation of experiments.
The intensity of the active state however it may be assessed is obviously an important property of the muscle; but it becomes extremely elusive if it is changing throughout a contraction. The problems are best illustrated by examples. Hill originally defined active state as the tension which the contractile element could bear without changing length; thus it could only be measured when the contractile element velocity was zero.
Even in skeletal muscle this was only easy when tension had reached a sustained maximum value in an isometric tetanus; in this situation the contractile element has moved right along the force-velocity curve Fig. If on the other hand the contraction is not steady, but takes the form of an isometric twitch in which the active state rises and then falls, it is obviously extremely unlikely that the contractile element would be brought to rest by the load just at the time when activity was maximal.
But unless this happens, the maximum recorded tension will not correspond to Po, and the intensity of the active state will be underestimated. The measurement is feasible if some means is devised to hold contractile element length constant, for example by controlled stretching of the muscle during the contraction; but the experimental difficulties are very great.
The cellular basis of the length-tension relation in cardiac muscle.
An alternative approach which to some extent added confusion, since it introduced another definition of active state has been to use the unloaded velocity of shortening as an index of active state. This is easier to examine experimentally; the muscle is released from its load at different points during successive twitch cycles and the velocity of shortening is measured immediately after the muscle has sprung back to unloaded length.
An example of the results obtained in such an experiment is shown in Fig. Time-course of active state in cardiac muscle as measured by released isotonic contractions. The arrow shows the time at which peak tension was achieved in an isometric twitch.
From Edman and Nilsson Recently, however, the techniques based on contractile element velocity have been shown to have a flaw because the duration of active state has been found to depend on length changes in the contractile element; if it shortens at any point in the contraction, the active state wanes earlier.
In recent experiments, therefore, the subject has been re-examined by a more sophisticated approach; the stress-strain characteristics of the series elastic element in a muscle are measured first, and then computer-controlled mechanical feedback is used to pull on the muscle during contraction so that it is continuously lengthened by just the amount necessary to keep the contractile element length constant; the tension on the muscle at each instant through the contraction cycle then defines the active state.
This method gives a time-course and intensity of active state which differ only a little from the isometric twitch response, the chief difference being a fractionally earlier rise and fall in active state. Even this, however, is unlikely to be the last word, because it has been demonstrated still more recently that the series elastic element has time-dependent properties, and the amount of stretch needed at different times in the cycle to fix contractile element length will therefore not depend solely on instantaneous tension.
These studies, culminating with the paradox that the contractility of a papillary muscle preparation is best defined by an experiment in which it is forced to lengthen, are described in some detail because they highlight the difficulties which arise in the experimental study of cardiac muscle mechanics at this level. It should by now be apparent that at least four variables - time, length, tension, and velocity - are important; and a whole range of extraneous factors which affect contractility such as temperature, oxygenation, and ionic environment need stringent control.
Blinks and Jewell have provided a useful recent survey of the subject; they point out that since the standard experiment explores the relationship between a pair of variables, six classes of experiment are needed to explore the inter-relationships between time, length, tension, and velocity.
We do not explore this subject in detail, but certain general conclusions are important enough to need stating. The inverse relationship shown to hold for skeletal muscle between developed force and velocity of shortening Fig.Cardiac muscle L T
This must be immediately qualified by pointing out that the force-velocity relationship is influenced by muscle-length and by the active state of the muscle. The effect of length can be predicted qualitatively from the length-tension relationship shown in Fig. Thus in order to present the properties of the muscle graphically, we would need a three-dimensional plot, with two of the axes being contractile element force and velocity as in Fig.
Then at any level of active state in the muscle, the various possible combinations of these would form a three-dimensional surface within the axes.
In practice, it is difficult to draw such graphs realistically, because they need to show both positive and negative velocities i. In trying to understand how the properties of the muscle interact, it is easier just to consider two types of contraction - isometric and isotonic. The simpler example is an isometric twitch, since it avoids muscle-length changes. The contraction starts at some point on the resting length-tension curve Fig.
Initially, the contractile element begins to shorten very fast, since it is relatively lightly loaded; thus velocity rapidly increases.
However, since shortening of the contractile element implies lengthening of the series elastic element, force builds up and the contractile element velocity is then reduced progressively until it becomes zero; at this point the maximum force equal to the sum of active plus resting tension in Fig.
This is the optimal resting length for producing the maximal tension. By increasing the muscle length beyond the optimum, the actin filaments become pulled away from the myosin filaments and from each other. At 3, there is little interaction between the filaments. Very few cross-bridges can form. Less tension is produced. When the filaments are pulled too far from one another, as seen in 4, they no longer interact and cross-bridges fail to form.
This principle demonstrates the length-tension relationship.
Chapter 11 part a
Maximal tension is readily produced in the body as the central nervous system maintains resting muscle length near the optimum. It does so by maintaining a muscle tone, i. The myofilaments are also elastic. They maintain enough overlap for muscular contraction. In cardiac muscles The length-tension relationship is also observed in cardiac muscles.
However, what differs in cardiac muscles compared to skeletal muscles is that tension increases sharply with stretching the muscle at rest slightly. This contrasts with the gradual build up of tension by stretching the resting skeletal muscle see Graph 4. Length-tension relationship observed in cardiac muscles. The optimum length is denoted as Lmax which is about 2.