Smooth muscle can be considered a general term for several types of tissue, each specially suited to particular functions. The challenge of the rheology of smooth muscle lies in the fact that it is "activity and relaxation intertwined" (Brady, 1977). Furthermore, the majority of smooth muscle exists as a component of an intricate composite, of which the mechanical properties are determined to a significant extent by the other components, such as collagen and elastin, and their configurations in the tissue.
The activity of smooth muscle can also add difficulty to mechanical testing. The ability of many visceral smooth muscles to contract spontaneously masks the passive tension. In addition, some smooth muscles are known to exhibit a myogenic response to stretch. Tracheal smooth muscle is one tissue that has been found to be particularly well suited for mechanical studies. According to N.L. Stephens (1975):
A firm groundwork in mechanical studies has been laid by Stephens, following the classical approach of Hill and Sonnenblick. There have also been many biochemical and pharmacological studies on tracheal smooth muscle, many of which use mechanical datum as an index of the effect of pharmacological agents. A phenomenological model of tracheal smooth muscle mechanical properties could serve as a tool in the interpretation of biochemical and pharmacological results.
The contractile properties have been characterized by force-velocity relationships under normal (Stephens, Kroeger, and H\Mehta, 1969) and hypoxic conditions (Stephens and Kroeger, 1970). The physical properties of the series elastic component (SEC) have been studied using quick-stretch and force-velocity measurement techniques (Stephens and Kromer, 1971). One study of the effects of temperature on force generation (Stephens et al, 1977) showed not only the expected change in the rate of active force generation, but also an increase in the stiffness of the SEC with decreased temperature.
The length-tension relationship of the unstimulated muscle has been used to describe the physical properties of the parallel elastic component. It was noted that, following an increase in length, the resting tension did not remain constant, but decreased with time, reaching a steady state usually within two minutes (Stephens, 1975).
Noting that there are sufficient differences among different smooth muscles, we can see that tracheal smooth muscle presents an ideal specimen for looking into the common features of smooth muscle rheology and, above all, for applying the methodology and the mentality that have been taught and demonstrated to us.
2. The Experimental SystemThe requirements that smooth muscle puts on the testing apparatus are unique. Forces need to be applied in the range from 50 mg to 50g, with resolution of 10 mg; specimen length has to be changed from 0.1mm to 10mm with resolution of 10um; and temperature needs to be adjusted from 5 C to 40 C, with a resolution of 0.05 C. The data acquisition requires programmable linear time, with temporal resolution of 10 ms; logarithmic time regimen up to five decades; and a multi channeled vector of data that includes time, position, force, and temperature. Furthermore, the system should be soft-ware oriented to provide easy access to a variety of loading regimens as well as their combinations in a preprogrammed sequence. The system should by quiet when the specimen is either at rest or at a programmed loading regimen, without instability or vibration that might stimulate muscle activity. Also, the viability of the muscle should be maintained. The other major requirement is that the system can be operated effectively yet simply. Features such as data file transmission, storage, and management, and data reduction and presentation are needed.
A system that was designed with these criteria, the Alphatron, has been constructed in our laboratory and used for the test of smooth muscle. A report of the instrument was recently published (Chen et al, 1985). A schematic of the system is shown in figure 5.1.
3. Reference LengthFor mechanical studies, a reliable reference length is needed with which deformations can be compared. One reference length, referred to in the literature as Lmax, or Lo, is determined experimentally as the length at which stimulation produces the maximum isometric tension. It represents the intrinsic optimal configuration of the muscle, independent of the geometry, and as such would be a good choice for a reference length. In tracheal smooth muscle, however, "the summit of the active tension curve is such that between 85% to 110% of standard muscle length Lo there is no significant change in the active tension" (Stephens, 1975). There is possibly a 25% error in the determination of Lmax. An uncertainty of this order of magnitude may render a reference length so determined unsuitable as a rheological parameter.
In studies of elasticity, the usual reference length used is the unstressed state. Biological soft tissues have an ill-defined unstressed state. Therefore efforts have been directed toward defining the unstressed state as nearly as possible. One such method uses the length of the tissue when hanging in solution, straightened by a 7.5 mg weight (Yin and Fung), 1971). At first glance, it seems that this method does not take into account variations in the specimen length or thickness, and no error estimate is possible.
A method has been demonstrated for assessing the unstressed state of mesentery (Chen, 1973). The unstressed state is taken as the average of the lengths of the specimen when under slight compression (i.e., slightly buckled,) and at the first sign of tension. The error, at most half of the difference of the buckled and slightly stressed length was reported to be 0.1 mm or 0.2% for the shortest specimen.
In a third method, the muscle is lengthened in successive increments of 0.2 mm until the first increase in force is indicated by the recording apparatus (Sparks and Bohr, 1962). The reference length, hence, depends on the sensitivity of the force-detecting apparatus used.
Our method is a two-point interpolation, with the first tension increase measured by the force transducer. A force change of 0.04 g is detectable. The length is increased from the lightly buckled length in increments of 0.127 mm. The length increase of 0.127 mm is the smallest length change that will produce a confidently measurable force change for our system. The reference length, denoted Lr, is the average of the lengths before and after the single movement that produces a sustained force change.
For a specimen length of 10 mm, this could entail as much as 0.6 % error, and the force at Lr could be anywhere between zero and 30 mg. Even though the method of Yin and Fung (1971) may seem to have drawbacks, the straightening load is very small, the state of stress is known precisely, and the error is well within the range afforded by ours or any other method.
4. ViabilityThe mechanical tests are performed in vitro, so the viability of the test specimen needs to be verified and maintained. If the muscle contracts vigorously when stimulated, it is considered viable.
At the beginning of the experiment, the length of the specimen is adjusted in increments of 0.127 mm until one gram of tension is indicated. As the muscle relaxes, the length is periodically increased to maintain the tension. The muscle is allowed to equilibrate for two hours at this length in continuously oxygenated Krebbs-Ringer bicarbonate-buffered (KRB) solution at a designated constant test temperature.
The equilibrated length of the specimen, called La, is recorded and used for viability tests. This length was recommended by Dr. N.L. Stephens as appropriate for equilibration and isometric viability tests since the length of tracheal smooth muscle of these approximate dimensions under one gram of tension is near the optimal length for activation. With the muscle still at La, the active state is induced by injecting Carbachol into the muscle chamber, giving a Carbachol concentration of 10-7 mole in the bathing solution. The time course of the contractile force is recorded (Figure 5.2). This establishes the initial viability of the specimen and sets a criterion, namely force generation, for subsequent viability tests. The viability of the specimen is again checked at the end of an experiment using the same conditions, (i.e., equilibration, the equilibrated length, temperature, stimulation, and bathing solution). If the force generated is at least 85% of that in the initial viability test, the data are considered valid.
5. The Passive StateThe passive state is often defined as the unstimulated state. In tissues that exhibit spontaneous contractions, there may be no quiescent unstimulated state. Measures have been taken to circumvent this problem by functionally inactivating the contractile system. Such methods include the use of myo-inhibitory substances, low temperatures, and removal of calcium from the tissue (Murphy, 1976; Lowy and Mulvany, 1973).
Even though tracheal smooth muscle does not exhibit any spontaneous activity, the unstimulated state may not be completely free of active tension. It was observed that the tension in the muscle in the low-calcium state at a given length is much less than the tension in the muscle at the same length in normal KRB solution.
For this study we approximate the passive state by the low-calcium state, The low-calcium state is achieved by equilibrating the specimen in calcium-free KRB solution. As shown in Figure 5.3, a test of the tissue response to Carbachol stimulation for varying calcium concentrations in the bathing medium showed the contractile force at a calcium concentrations of 2.5 x 10-5 mmol to be less than 3% of that in normal KRB (pCa 0.4 mmol). The muscle seems able to tolerate the low-calcium state for long periods of time without apparent damage, since, when the tissue is returned to the normal KRB solution after several hours in the calcium-free solution, it is able to contract with nearly as much vigor as before the low-calcium state. For tests in the passive state, the muscle and muscle chamber are rinsed with a 2.0 mmol EGTA KRB solution before the calcium-free solution is introduced into the chamber. The EGTA solution is not used during the tests in the passive state because the tissue, it seems, cannot tolerate this solution for long periods. The so-called calcium-free solution is not completely free of calcium because of impurities in the reagents and deionized water used and also because some calcium may leach out of the tissue.
For tests that require longer periods of time in the passive state, the low-calcium state is easier to use that the repeated administration of quickly metabolized drugs, such as epinephrine. As we view the smooth muscle sample as a polymeric material, the effects of the temperature are twofold. The low temperatures used to inhibit muscle activity may not only affect the rate of metabolism of the muscle but may also change the rheology of the component polymers. The passive properties of the tissue at low temperature might not apply to the tissue at physiological temperatures.
There are two categories of tests that are performed on the tissue in the passive state: tests exploring the stress-strain-history relationship--such as the steady-state length-tension test, the relaxation test, and the cyclic elongation--and tests exploring the dependence of the passive behavior on temperature.
6. ReproducibilitySince several tests will be performed on the same tissue sample, it is important to determine how the tissue response is affected by previous tests. Usually preconditioning is used to achieve reproducibility. In preconditioning the specimen, several cycles of the intended test are performed at short intervals until the response becomes reproducible. One unique feature of tracheal smooth muscle is that it seems to recover completely after a test, so reproducibility could be achieved without preconditioning.
In order to test the repeatability of the passive behavior, a series of the same test was performed at decreasing intervals of rest. Figures 5.4 and 5.5 show the results of a succession of cyclic elongation tests. The results of a succession of relaxation tests is shown in Figure 5.6. It was found that the tissue will recover completely and the results are reproducible as long as enough time is allowed between tests: 15-30 minutes after relaxation tests, and 5-10 minutes after cyclic elongation, depending on the extent of elongation.
Elongations of more than 40% of Lr at rapid rates seem to damage the tissue because, shortly after several of these tests, there is a slow rise in the tension at Lr, even in the calcium-free solution. The rise in tension has been observed to exceed the previously recorded near-zero tension at Lr by as much as one-half gram weight, without showing any tendency to level off after three hours.
7. The Viscoelastic BehaviorA relaxation with normalized force verses logarithmic time is shown in Figure 5.7. It is noted that the stress relaxation is very rapid, with a well-defined steady-state residual tension, usually between 5 and 10% of the recorded initial tension, reached within 200 seconds. The muscle has also been shown to recover completely after elongation. It seems plausible to consider the tracheal smooth muscle, in the passive state, as a viscoelastic solid. A temperature change from 37 to 27 C does not appear to have an appreciable effect on the time scale of stress relaxation, and relaxation has also been found to be indifferent to the extent of elongation.
The elastic response was studied by two tests: the cyclic elongation and the steady-state length-tension test. Both the steady-state length-tenth relationship, as shown in Figure 5.8, and the hysteresis, as shown in Figure 5.9, show a nonlinear relationship between stress and stretch ratio. A mathematical model is needed to describe the elastic response. It appears to be either an exponential relationship, similar to that found for the ureter (Yin and Fung, 1971) and the mesentery (Fung, 1967), or a power law relationship as found in the taenia coli smooth muscle (Price et al, 1979).
Since stress relaxation is quite rapid in this material, it may interfere significantly with the stress increase during elongation. As a consequence, the apparent stress-strain relation is rate-dependent, and, it may not be advisable to approximate the instantaneous elastic response by the apparent stress-strain relationship. However, as there is a steady-state residual stress obtainable within a relatively short time, the rubbery elastic response could be used as the kernel in the formulation of a viscoelastic model.
8. Temperature EffectTracheal smooth muscle can be considered as a polymeric system composed of collagen, elastin, and myofilaments in a network, filled with amorphous ground substance. The rheology of most polymeric materials depends on temperature, and we have observed a temperature effect on the rheology of the smooth muscle in the passive state.
One of the tests on the effect of temperature on the passive behavior of the tracheal smooth muscle is to measure the residual isometric tension during a change in the temperature. Figure 5.10 shows the time course of the changes of stress and temperature for such an experiment. At the start of the test, the specimen in the passive state was lengthened to a stretch ratio of 1.30. After the stress relaxation was complete, the temperature was lowered from 37 C to 17 C, and back to 37 C, continuously over a period of two hours. There was a slight reduction in the force as the temperature decreased, but as the temperature was increased, the tension rose almost exponentially, quickly exceeding the resting tension previously recorded at 37 C by almost sevenfold.
Apparently the increase in tension was produced by some active mechanism induced by the change of temperature. Activity induced by the change of temperature had been reported for intestinal smooth muscle in a review by Prosser (1974), and the effects of change of temperature on the membrane potential in smooth muscles has been documented by Magaribuchi et al (1973). Attempts were made to remove more calcium from the muscle using chelating agents, but the chelating agents themselves produced other activation artifacts. Epinephrine had no effect on the temperature-induced activity.
Assuming that the muscle activity was induced by the combined effect of the change of temperature and tension, the temperature effect was, instead, investigated by allowing the specimen to equilibrate at Lr at various temperatures before performing the same series of relaxation and cyclic elongation tests. Thus the effects of temperature and the effects of the change of temperature are separated. As the temperature decreased from 37 C to 27 C, the stiffness of the tissue, as shown in Figure 5.11, decreased by 54% plus or minus 8%. This follows the same trend of temperature dependence found in resting striated muscle (Hill, 1952). From the network theory of rubber, the elastic constant, G, is represented as a function of the absolute temperature, T, by the equation (Treloar, 1967):
where N is the number of molecular chains per unit volume, and k is the Boltzman constant. The temperature change from 37 C to 27 C represents a 3.33% change in stiffness and could not explain the 54% change found in the stiffness of the smooth muscle. It has been suggested that the phenomenological theory of rubber elasticity could be more applicable to living tissues (Fung, 1972). One of the challenges is to build a unified theoretical model to explain both time- and temperature-dependence.
9. ClosureA smooth muscle specimen has been found that has a one-dimensional structural geometry; that exhibits no spontaneous rhythmic contractile activity, nor manifests myogenic activity; and that can be easily obtained, kept viable during long experiments, and rendered passive. An experimental system has been constructed with the characteristics needed for the study of the mechanical properties of the smooth muscle. It has been observed that the passive properties of tracheal smooth muscle are time- and temperature-dependent.
The classical model of muscle results from two dichotomies. Based upon observation, the first dichotomy gives the muscle a passive element and an active element. The second dichotomy further cuts the active element into a contractile element and a series element, the contractile element being responsible for the length change and the series element being responsible for the generation of force. Clearly, the second dichotomy is one of convenience, since it is not based on either theoretical requirements or observations. The rapid relaxation of the tracheal muscle in the passive state indicates that is might not be fitted into this classical three-element framework. The smooth muscle behavior is activity- and viscoelasticity-intertwined. For, while the muscle is in activation, it is simultaneously in rapid relaxation. And a clear-cut active state might be difficult to define. Hence the promises and challenges would lie in the interpretation and analysis of the data and in the formulation of a model to describe smooth muscle behavior in both the passive and active states.
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