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Mechanics of Vascular Smooth Muscle

R. A. Murphy

10.1002/cphy.cp020213

Source: Supplement 7: Handbook of Physiology, The Cardiovascular System, Vascular Smooth Muscle

Originally published: 1980

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Uses of Mechanical Studies and Analytical Framework
1.1 Purposes and Scope of Chapter
1.2 Analytical Framework of Classic Muscle Mechanics
2 Preparations and Normalization
2.1 Criteria for Preparations Used in Mechanical Studies
2.2 Suitable Tissue Preparations and Procedures
2.3 Definitions, Units, and Symbols
3 Mechanics of Vascular Smooth Muscle Tissues
3.1 Parallel Elastic Component and Mechanical Hysteresis
3.2 Series Elastic Component
3.3 Static Properties of the Contractile Component
3.4 Dynamic Properties of the Contractile Component
4 Applicability of Tissue Mechanics to Cells and the Contractile Component
4.1 Relationships Between Cell and Tissue Mechanics
Figure 1. Figure 1.

Common representations of mechanical properties of muscle. A: generalized apparatus for mechanical measurements. When the lower stop is in place, measurement is isometric (constant length). Activation of solenoid portion of lower stop provides a quick release, converting isometric response into isotonic (constant load) contraction. B: isometric force as a function of length in relaxed (dotted curve) and maximally stimulated (dashed curve) muscle. Difference between these curves (solid curve) reflects active force development. Maximal force (F0) is developed at the optimal length for force development (L0). C: comparison of isotonic and isometric contractions. Upper left curve is isometric force when no shortening can occur. Lower left curves show that the amount of shortening and shortening velocity increase as load is diminished. This dependence is plotted (right curve) as the force‐velocity relationship, with an extension of the data to situations in which the contracting muscle is forcibly stretched. D: if isometrically contracting muscle is subjected to quick release, active shortening is preceded by elastic recoil (partially obscured by inertial oscillations). From this recoil the elastic extension of contractile material and other elements in series with the contractile material can be plotted as load‐extension curve.
Figure 2. Figure 2.

Analogue models of muscle. Simple two‐component model is shown on the left. A: three‐component system arranged as in Maxwell element (a). B: model with the three components in Voigt element (b) configuration. C and D: more complicated four‐component models. sec, Series elastic component; pec, parallel elastic component; cc, contractile component.

From Simmons and Jewell 112
Figure 3. Figure 3.

Relationships between tension development by pig carotid artery strips and tissue geometry. A: graph showing records of mechanical tension elicited by norepinephrine (10−6 M) vs. oxygen partial pressure in the solution. Arrows placed at points that reflect the minimal solution Po2 that could sustain full force development. Numbers above the arrows are strip thicknesses in centimeters. B: graph showing best fit for the data obtained, in which the limiting solution Po2 is plotted against the square of one‐half tissue thickness (a′), with α′ used to indicate that tissue geometry was corrected because the strips were not infinite sheets. Equation shows the theoretical relationship between critical Po2 for cell in the center of strip (Po2cell) and the solution Po2 in an infinite sheet (Po2s), assuming diffusion limitation of O2 is responsible for the mechanical tension reduction. M, metabolic rate; a′, one‐half tissue thickness (in infinite sheet); D, diffusion coefficient for oxygen.

Adapted from Pittman and Duling 99
Figure 4. Figure 4.

Stress‐strain behavior of various types of materials. A: extension of pure elastic material is proportional only to stress. B: addition of viscous drag leads to hysteresis and time‐dependent properties. C: tissues usually show complex behavior as indicated by the hysteresis loop. Studies of smooth muscle often involve an isotonic release from a fixed length (horizontal arrow) with accompanying length changes that are a function of time (creep). Alternatively, tissue may be initially stretched to some fixed length, and isometric force declines with time (vertical arrow, stress‐relaxation).

From Alexander 5. Reprinted from Federation Proceedings
Figure 5. Figure 5.

Estimation of passive elasticity of smooth muscle. A: change in force (Fm) and length in stimulated skeletal muscle released to a shorter, constant length is indicated in the top two graphs. Corresponding length changes in the parallel elastic component (pec), series elastic component (sec), and contractile component (cc) are indicated below. ΔLm, change in muscle length; ΔLpec, change in length of parallel elastic component; ΔLsec, change in length of series elastic component; ΔLcc, change in length of contractile component. B: hanges in force (F) observed after step length (L) changes of unstimulated pig carotid media tissue possessing some degree of tone. Three protocols for length changes are indicated in curves a, b, and c, in which the final length was always 9.0 mm. Response of unstimulated smooth muscles upon release was similar to that of stimulated skeletal muscle in A. Minimal force observed at 9.0 mm varied, with Fa > Fb > Fc. C: force‐length curves (a, b, and c) were obtained using the protocols (a, b, and c, respectively) depicted in B. Curve d was obtained using protocol c after overnight equilibration in calcium‐free solution. Force on the ordinate is expressed as a fraction of maximal active force at optimal length for force development (L0). Protocol c appears to reflect true passive length‐force properties for this tissue. F0, maximal active force.

A from Simmons and Jewell 112; B and C from Herlihy and Murphy 56, by permission of the American Heart Association, Inc
Figure 6. Figure 6.

Suggested model for arrangement of dense bodies (solid circles) connected by relatively inelastic 10‐nm intermediate filaments (straight lines) in a smooth muscle cell. Stretching causes an increase in fiber length (A to B), with axial consolidation of network seen in cross section (a to b) as a result of reorientation of the filaments linking dense bodies. Results are based on electron micrographs of extracted taenia coli fibers.

From Cooke and Fay 27
Figure 7. Figure 7.

Isotonic release of contracting skeletal muscle to low constant load. Length of the series elastic component (sec) changes very rapidly because of elastic recoil, with further changes in muscle length reflecting shortening of the contractile component (cc). Fm, muscle force; ΔLm, change in muscle length; ΔLsec, change in sec length; ΔLcc, change in cc length.

From Simmons and Jewell 112
Figure 8. Figure 8.

Length‐force curves for pig carotid media. Solid lines give experimental data that Herlihy and Murphy obtained 56,57 for active force developed as a fraction of optimal tissue length, for the PEC, and for extension of the SEC. Dashed line and upper abscissa represent correction for length of contractile system after shortening against SEC. Dotted extensions of this corrected curve are linear extrapolations to zero force. PEC, parallel elastic component; SEC, series elastic component; F, force; F0, maximal force; L, length; L0, optimal length for force development.

From Murphy 88, with permission of S. Karger AG, Basel
Figure 9. Figure 9.

Isometric force (lever fixed) and isotonic shortening (against preload equal to passive force) in spontaneously contracting rat portal vein. A: muscle length was 3 mm and passive force (and preload) was 4 × 10−4 N. B: muscle was stretched to 3.8 mm, with increase in passive force (and preload) to 35 × 10−4 N. C: vertical arrows indicate isometric force development at two lengths, and horizontal arrows show isotonic shortening. D: Maxwell 7 and Voigt (II) analogue models. F, force; L, length.

From Johansson 68. Reprinted from Federation Proceedings
Figure 10. Figure 10.

Effect of wall thickness on geometrical artifacts in simple tissue preparations. Illustrated vessel ring has ri:r0 ratio of 0.5. Were such a ring opened, tissue would assume trapezoidal shape if no outside stresses were imposed. Because mounting procedures tend to yield a tissue with more rectangular section, resulting stresses produce a variation in fiber length (or in stress distribution) whose maximal extent can be estimated from graph. ri, Inner radius; r0, outer radius; Δ, variation; α, (outer circumference – inner circumference)/2; b, mean circumference.
Figure 11. Figure 11.

Comparison of length‐force relationships in skeletal and smooth muscle. Solid line, sarcomere length‐force data from electrically stimulated single frog semitendinosus fibers 49. Dashed line indicates minimal estimate for force (F) development in skinned semitendinosus fibers when stimulated by Ca2+ at short lengths 108. Solid circles represent more realistic estimates 108. Frog skeletal muscle data were normalized to sarcomere length of 2.1 μm. In smooth muscles L0 represents length at which maximal isometric force (F0) was obtained. Open circles, pig carotid media 56; open squares, cat duodenyl circular 86; stars, dog trachealis 121.

From Murphy 88, with permission of S. Karger, AG, Basel
Figure 12. Figure 12.

Force‐velocity data. A: curve according to Hill's equation, which is (P + a) (V + b) = (P0 + a)b, where P is load on muscle, P0 is maximal isometric force, V is shortening velocity, a is a constant with dimensions of force, and b is a constant with dimensions of length. B: curve acording to Aubert's equation, which is P = (P0 + F) exp (–V/B) – F, where F and B are constants. Original notation using P and P0 instead of F and F0 is retained in this figure. There are various ways of determining constants of these equations, but if data are rather scattered the best method is to make use of corresponding linear equations. C: curve according to Hill's equation, (P0 – P)/V = (P/b) + (a/b). D: curve acording to Aubert's equation, loge (P + F) = loge (P0 + F) – (V/B). To obtain values for a and b of the Hill equation, the best straight line is drawn through a plot of (P0 – P)/V against P. Constants can then be obtained as shown from slope of the line and its intercept on force axis. See Reference 112 to obtain values for B and F of Aubert's equation (B and D). Note that in C the high force values tend to have too big an influence in determining position of the line, whereas in D it is high‐velocity values that dominate. Because both equations have three constants, the curve‐fitting procedure involves loss of three degrees of freedom from data (i.e., equivalent of three data points). If there are only three data points, then curves drawn according to either equation must pass through these three points. It follows that judgments about fitting the data by the equations can be made only if there are substantially more data points.

From Simmons and Jewell 112
Figure 13. Figure 13.

Force‐velocity data for pig carotid media. Solid lines were obtained by the quick‐release method for initial shortening velocity as function of load in electrically stimulated tissues. Power output (curve starting at origin) was obtained as product of force/cross‐sectional area and velocity 57. Dashed line represents results obtained from potassium‐stimulated tissues (J. T. Herlihy, unpublished observations). L0, optimal length for force development.

From Murphy 88, with permission of S. Karger AG, Basel
Figure 14. Figure 14.

Three‐dimensional representation of dynamic length‐force‐velocity phase space of contractile component. Data were obtained using rat gracilis anticus muscle at 17.5°C. L′, calculated length of the contractile component after correction for the series elastic component; L'0, calculated optimal length for force development; F, force; F0, maximal force.

From Bahler et al. 16
Figure 15. Figure 15.

Tentative three‐dimensional diagram illustrating force‐velocity curves of contractile elements in vascular smooth muscle at different muscle lengths with maximal (full lines) and submaximal (broken lines) activation of contractile machinery. Heavy line in the zero velocity plane represents the relationship between length and active force at maximal contraction. Dotted lines below the zero velocity (or force‐length) plane illustrate possible relationships between force and lengthening velocity when contracted muscle is stretched by forces greater than maximal force. V, velocity; L, length; F, force.

From Johansson 69
Figure 16. Figure 16.

Force‐velocity plots at beginning of isotonic movements in cat soleus muscle. Plotted values of velocity were those measured 15 m/s after release of isometrically contracting muscle to load corresponding to scale on ordinate. Initial length of muscle was constant. Velocity at which muscle lengthens under an imposed load is not constant but varies with load, stimulation frequency, and other factors. Stimulation frequencies (pulses/s, designated by pps) are indicated to the left of each curve.

From Joyce and Rack 75
Figure 17. Figure 17.

Different arrangements of six axially oriented cells anatomically in series (small solid boxes) comprising a constant fraction of tissue cross‐sectional area. A: cells linked in series. B and C: series and parallel linkages. D: cells all in parallel. Thin lines indicate stiff force‐transmitting structures. Microscopic examination would not necessarily distinguish these arrangements in tissue. Table gives effect of model on tissue force developed (FT)/cell force developed (FC), tissue shortening (FT)/cell shortening (SC), and tissue shortening velocity (VT)/cell shortening velocity (VC). Critical (tissue) segment indicates minimal tissue segment length (relative units) at which force per cross‐sectional area remains independent of overall tissue length.

From Driska and Murphy 37, with permission of S. Karger AG, Basel


Figure 1.

Common representations of mechanical properties of muscle. A: generalized apparatus for mechanical measurements. When the lower stop is in place, measurement is isometric (constant length). Activation of solenoid portion of lower stop provides a quick release, converting isometric response into isotonic (constant load) contraction. B: isometric force as a function of length in relaxed (dotted curve) and maximally stimulated (dashed curve) muscle. Difference between these curves (solid curve) reflects active force development. Maximal force (F0) is developed at the optimal length for force development (L0). C: comparison of isotonic and isometric contractions. Upper left curve is isometric force when no shortening can occur. Lower left curves show that the amount of shortening and shortening velocity increase as load is diminished. This dependence is plotted (right curve) as the force‐velocity relationship, with an extension of the data to situations in which the contracting muscle is forcibly stretched. D: if isometrically contracting muscle is subjected to quick release, active shortening is preceded by elastic recoil (partially obscured by inertial oscillations). From this recoil the elastic extension of contractile material and other elements in series with the contractile material can be plotted as load‐extension curve.



Figure 2.

Analogue models of muscle. Simple two‐component model is shown on the left. A: three‐component system arranged as in Maxwell element (a). B: model with the three components in Voigt element (b) configuration. C and D: more complicated four‐component models. sec, Series elastic component; pec, parallel elastic component; cc, contractile component.

From Simmons and Jewell 112


Figure 3.

Relationships between tension development by pig carotid artery strips and tissue geometry. A: graph showing records of mechanical tension elicited by norepinephrine (10−6 M) vs. oxygen partial pressure in the solution. Arrows placed at points that reflect the minimal solution Po2 that could sustain full force development. Numbers above the arrows are strip thicknesses in centimeters. B: graph showing best fit for the data obtained, in which the limiting solution Po2 is plotted against the square of one‐half tissue thickness (a′), with α′ used to indicate that tissue geometry was corrected because the strips were not infinite sheets. Equation shows the theoretical relationship between critical Po2 for cell in the center of strip (Po2cell) and the solution Po2 in an infinite sheet (Po2s), assuming diffusion limitation of O2 is responsible for the mechanical tension reduction. M, metabolic rate; a′, one‐half tissue thickness (in infinite sheet); D, diffusion coefficient for oxygen.

Adapted from Pittman and Duling 99


Figure 4.

Stress‐strain behavior of various types of materials. A: extension of pure elastic material is proportional only to stress. B: addition of viscous drag leads to hysteresis and time‐dependent properties. C: tissues usually show complex behavior as indicated by the hysteresis loop. Studies of smooth muscle often involve an isotonic release from a fixed length (horizontal arrow) with accompanying length changes that are a function of time (creep). Alternatively, tissue may be initially stretched to some fixed length, and isometric force declines with time (vertical arrow, stress‐relaxation).

From Alexander 5. Reprinted from Federation Proceedings


Figure 5.

Estimation of passive elasticity of smooth muscle. A: change in force (Fm) and length in stimulated skeletal muscle released to a shorter, constant length is indicated in the top two graphs. Corresponding length changes in the parallel elastic component (pec), series elastic component (sec), and contractile component (cc) are indicated below. ΔLm, change in muscle length; ΔLpec, change in length of parallel elastic component; ΔLsec, change in length of series elastic component; ΔLcc, change in length of contractile component. B: hanges in force (F) observed after step length (L) changes of unstimulated pig carotid media tissue possessing some degree of tone. Three protocols for length changes are indicated in curves a, b, and c, in which the final length was always 9.0 mm. Response of unstimulated smooth muscles upon release was similar to that of stimulated skeletal muscle in A. Minimal force observed at 9.0 mm varied, with Fa > Fb > Fc. C: force‐length curves (a, b, and c) were obtained using the protocols (a, b, and c, respectively) depicted in B. Curve d was obtained using protocol c after overnight equilibration in calcium‐free solution. Force on the ordinate is expressed as a fraction of maximal active force at optimal length for force development (L0). Protocol c appears to reflect true passive length‐force properties for this tissue. F0, maximal active force.

A from Simmons and Jewell 112; B and C from Herlihy and Murphy 56, by permission of the American Heart Association, Inc


Figure 6.

Suggested model for arrangement of dense bodies (solid circles) connected by relatively inelastic 10‐nm intermediate filaments (straight lines) in a smooth muscle cell. Stretching causes an increase in fiber length (A to B), with axial consolidation of network seen in cross section (a to b) as a result of reorientation of the filaments linking dense bodies. Results are based on electron micrographs of extracted taenia coli fibers.

From Cooke and Fay 27


Figure 7.

Isotonic release of contracting skeletal muscle to low constant load. Length of the series elastic component (sec) changes very rapidly because of elastic recoil, with further changes in muscle length reflecting shortening of the contractile component (cc). Fm, muscle force; ΔLm, change in muscle length; ΔLsec, change in sec length; ΔLcc, change in cc length.

From Simmons and Jewell 112


Figure 8.

Length‐force curves for pig carotid media. Solid lines give experimental data that Herlihy and Murphy obtained 56,57 for active force developed as a fraction of optimal tissue length, for the PEC, and for extension of the SEC. Dashed line and upper abscissa represent correction for length of contractile system after shortening against SEC. Dotted extensions of this corrected curve are linear extrapolations to zero force. PEC, parallel elastic component; SEC, series elastic component; F, force; F0, maximal force; L, length; L0, optimal length for force development.

From Murphy 88, with permission of S. Karger AG, Basel


Figure 9.

Isometric force (lever fixed) and isotonic shortening (against preload equal to passive force) in spontaneously contracting rat portal vein. A: muscle length was 3 mm and passive force (and preload) was 4 × 10−4 N. B: muscle was stretched to 3.8 mm, with increase in passive force (and preload) to 35 × 10−4 N. C: vertical arrows indicate isometric force development at two lengths, and horizontal arrows show isotonic shortening. D: Maxwell 7 and Voigt (II) analogue models. F, force; L, length.

From Johansson 68. Reprinted from Federation Proceedings


Figure 10.

Effect of wall thickness on geometrical artifacts in simple tissue preparations. Illustrated vessel ring has ri:r0 ratio of 0.5. Were such a ring opened, tissue would assume trapezoidal shape if no outside stresses were imposed. Because mounting procedures tend to yield a tissue with more rectangular section, resulting stresses produce a variation in fiber length (or in stress distribution) whose maximal extent can be estimated from graph. ri, Inner radius; r0, outer radius; Δ, variation; α, (outer circumference – inner circumference)/2; b, mean circumference.



Figure 11.

Comparison of length‐force relationships in skeletal and smooth muscle. Solid line, sarcomere length‐force data from electrically stimulated single frog semitendinosus fibers 49. Dashed line indicates minimal estimate for force (F) development in skinned semitendinosus fibers when stimulated by Ca2+ at short lengths 108. Solid circles represent more realistic estimates 108. Frog skeletal muscle data were normalized to sarcomere length of 2.1 μm. In smooth muscles L0 represents length at which maximal isometric force (F0) was obtained. Open circles, pig carotid media 56; open squares, cat duodenyl circular 86; stars, dog trachealis 121.

From Murphy 88, with permission of S. Karger, AG, Basel


Figure 12.

Force‐velocity data. A: curve according to Hill's equation, which is (P + a) (V + b) = (P0 + a)b, where P is load on muscle, P0 is maximal isometric force, V is shortening velocity, a is a constant with dimensions of force, and b is a constant with dimensions of length. B: curve acording to Aubert's equation, which is P = (P0 + F) exp (–V/B) – F, where F and B are constants. Original notation using P and P0 instead of F and F0 is retained in this figure. There are various ways of determining constants of these equations, but if data are rather scattered the best method is to make use of corresponding linear equations. C: curve according to Hill's equation, (P0 – P)/V = (P/b) + (a/b). D: curve acording to Aubert's equation, loge (P + F) = loge (P0 + F) – (V/B). To obtain values for a and b of the Hill equation, the best straight line is drawn through a plot of (P0 – P)/V against P. Constants can then be obtained as shown from slope of the line and its intercept on force axis. See Reference 112 to obtain values for B and F of Aubert's equation (B and D). Note that in C the high force values tend to have too big an influence in determining position of the line, whereas in D it is high‐velocity values that dominate. Because both equations have three constants, the curve‐fitting procedure involves loss of three degrees of freedom from data (i.e., equivalent of three data points). If there are only three data points, then curves drawn according to either equation must pass through these three points. It follows that judgments about fitting the data by the equations can be made only if there are substantially more data points.

From Simmons and Jewell 112


Figure 13.

Force‐velocity data for pig carotid media. Solid lines were obtained by the quick‐release method for initial shortening velocity as function of load in electrically stimulated tissues. Power output (curve starting at origin) was obtained as product of force/cross‐sectional area and velocity 57. Dashed line represents results obtained from potassium‐stimulated tissues (J. T. Herlihy, unpublished observations). L0, optimal length for force development.

From Murphy 88, with permission of S. Karger AG, Basel


Figure 14.

Three‐dimensional representation of dynamic length‐force‐velocity phase space of contractile component. Data were obtained using rat gracilis anticus muscle at 17.5°C. L′, calculated length of the contractile component after correction for the series elastic component; L'0, calculated optimal length for force development; F, force; F0, maximal force.

From Bahler et al. 16


Figure 15.

Tentative three‐dimensional diagram illustrating force‐velocity curves of contractile elements in vascular smooth muscle at different muscle lengths with maximal (full lines) and submaximal (broken lines) activation of contractile machinery. Heavy line in the zero velocity plane represents the relationship between length and active force at maximal contraction. Dotted lines below the zero velocity (or force‐length) plane illustrate possible relationships between force and lengthening velocity when contracted muscle is stretched by forces greater than maximal force. V, velocity; L, length; F, force.

From Johansson 69


Figure 16.

Force‐velocity plots at beginning of isotonic movements in cat soleus muscle. Plotted values of velocity were those measured 15 m/s after release of isometrically contracting muscle to load corresponding to scale on ordinate. Initial length of muscle was constant. Velocity at which muscle lengthens under an imposed load is not constant but varies with load, stimulation frequency, and other factors. Stimulation frequencies (pulses/s, designated by pps) are indicated to the left of each curve.

From Joyce and Rack 75


Figure 17.

Different arrangements of six axially oriented cells anatomically in series (small solid boxes) comprising a constant fraction of tissue cross‐sectional area. A: cells linked in series. B and C: series and parallel linkages. D: cells all in parallel. Thin lines indicate stiff force‐transmitting structures. Microscopic examination would not necessarily distinguish these arrangements in tissue. Table gives effect of model on tissue force developed (FT)/cell force developed (FC), tissue shortening (FT)/cell shortening (SC), and tissue shortening velocity (VT)/cell shortening velocity (VC). Critical (tissue) segment indicates minimal tissue segment length (relative units) at which force per cross‐sectional area remains independent of overall tissue length.

From Driska and Murphy 37, with permission of S. Karger AG, Basel
References
 1. Abbott, B. C., and X. M. Aubert. The force exerted by active striated muscle during and after change of length. J. Physiol. London 117: 77–86, 1952.
 2. Abbott, B. C., and D. G. Gordon. A commentary on muscle mechanics. Circulation Res. 36: 1–7, 1975.
 3. Abbott, B. C., and J. Lowy. Stress relaxation in muscle. Proc. Roy. Soc. London Ser. B 146: 281–288, 1957.
 4. Åberg, A. K. G. The series elasticity of active taenia coli in vitro. Acta Physiol. Scand. 69: 348–354, 1967.
 5. Alexander, R. S. Viscoelastic determinants of muscle contractility and “cardiac tone.” Federation Proc. 21: 1001–1005, 1962.
 6. Alexander, R. S. Critical closure reexamined. Circulation Res. 40: 531–536, 1977.
 7. Apter, J. T. Correlation of visco‐elastic properties with microscopic structure of large arteries. IV. Thermal responses of collagen, elastin, smooth muscle, and intact arteries. Circulation Res. 21: 901–918, 1967.
 8. Ashton, F. T., A. V. Somlyo, and A. P. Somlyo. The contractile apparatus of vascular smooth muscle: intermediate high voltage stereo electron microscopy. J. Mol. Biol. 98: 17–29, 1975.
 9. Attinger, F. M. L. Two‐dimensional in‐vitro studies of femoral arterial walls of the dog. Circulation Res. 22: 829–840, 1968.
 10. Aubert, X. Le couplage énergétique de la contraction musculaire (Thèse d'agrégation, Catholic University of Louvain). Brussels: Editions Ascia, 1956.
 11. Axelsson, J. Mechanical properties of smooth muscle, and the relationship between mechanical and electrical activity. In: Smooth Muscle, edited by E. Bülbring, A. F. Brading, A. W. Jones, and T. Tomita. Baltimore: Williams & Wilkins, 1970, p. 289–315.
 12. Azuma, T., and M. Hasegawa. A rheological approach to the architecture of arterial walls. Japan. J. Physiol. 21: 27–47, 1971.
 13. Bagby, R. M. Time course of isotonic contraction in single cells and muscle strips from Bufo marinus stomach. Am. J. Physiol. 227: 789–793, 1974.
 14. Bagby, R. M., and B. A. Fisher. Graded contractions in muscle strips and single cells from Bufo marinus stomach. Am. J. Physiol. 225: 105–109, 1973.
 15. Bagby, R. M., A. M. Young, R. S. Dotson, B. A. Fisher, and K. McKinnon. Contraction of single smooth muscle cells from Bufo marinus stomach. Nature 234: 351–352, 1971.
 16. Bahler, A. S., J. T. Fales, and K. Zierler. The dynamic properties of mammalian skeletal muscle. J. Gen. Physiol. 51: 369–384, 1968.
 17. Bárány, M. ATPase activity of myosin correlated with speed of muscle shortening. J. Gen. Physiol. 50: 197–218, 1967.
 18. Barr, L., V. E. Headings, and D. F. Bohr. Potassium and the recovery of arterial smooth muscle after cold storage. J. Gen. Physiol. 46: 19–33, 1962.
 19. Bevan, J. A. Some characteristics of the isolated sympathetic nerve‐pulmonary artery preparation of the rabbit. J. Pharmacol. Exptl. Therap. 137: 213–218, 1962.
 20. Bevan, J. A., and J. V. Osher. A direct method for recording tension changes in the wall of small blood vessels in vitro. Agents Actions 2: 257–260, 1972.
 21. Blinks, J. R., and B. R. Jewell. The meaning and measurement of myocardial contractility. In: Cardiovascular Fluid Dynamics, edited by D. H. Bergel. New York: Academic, 1972, vol. 1, p. 225–260.
 22. Bozler, E. Plasticity of contractile elements of muscle as studied in extracted muscle fibers. Am. J. Physiol. 171: 359–364, 1952.
 23. Butler, T. M., M. J. Siegman, and R. E. Davies. Rigor and resistance to stretch in vertebrate smooth muscle. Am. J. Physiol. 231: 1509–1514, 1976.
 24. Carrier, O.Jr., J. R. Walker, and A. C. Guyton. Role of oxygen in autoregulation of blood flow in isolated vessels. Am. J. Physiol. 206: 951–954, 1964.
 25. Close, R. I. Dynamic properties of mammalian skeletal muscles. Physiol. Rev. 52: 129–197, 1972.
 26. Cooke, P. A filamentous cytoskeleton in vertebrate smooth muscle fibers. J. Cell Biol. 68: 539–556, 1976.
 27. Cooke, P. H., and F. S. Fay. Correlation between fiber length, ultrastructure, and the length‐tension relationship of mammalian smooth muscle. J. Cell Biol. 52: 105–116, 1972.
 28. Curtin, N. A., and R. E. Davies. Chemical and mechanical changes during stretching of activated frog skeletal muscle. Cold Spring Harbor Symp. Quant. Biol. 37: 619–626, 1972.
 29. Daniel, E. E., and D. M. Paton (editors). Methods in Pharmacology. Smooth Muscle. New York: Plenum, 1975, vol. 3.
 30. Davey, D. F., C. L. Gibbs, and H. C. McKirdy. Structural, mechanical and myothermic properties of rabbit rectococcygeus muscle. J. Physiol. London 248: 207–230, 1975.
 31. Detar, R., and D. F. Bohr. Oxygen and vascular smooth muscle contraction. Am. J. Physiol. 214: 241–244, 1968.
 32. Dobrin, P. B. Influence of initial length on length‐tension relationship of vascular smooth muscle. Am. J. Physiol. 225: 664–670, 1973.
 33. Dobrin, P. B. Vascular muscle series elastic element stiffness during isometric contraction. Circulation Res. 34: 242–250, 1974.
 34. Dobrin, P. B., and T. R. Canfield. Series elastic and contractile elements in vascular smooth muscle. Circulation Res. 33: 454–464, 1973.
 35. Dobrin, P. B., and T. Canfield. Identification of smooth muscle series elastic component in intact carotid artery. Am. J. Physiol. 232: H122–H130, 1977 or
 36. Am. J. Physiol.: Heart Circ. Physiol. 1: H122–H130, 1977.
 37. Driska, S. P., D. N. Damon, and R. A. Murphy. Estimates of cellular mechanics in an arterial smooth muscle. Biophys. J. 24: 525–540, 1978.
 38. Driska, S. P., and R. A. Murphy. An estimate of cellular force generation in an arterial smooth muscle with a high actin: myosin ratio. Blood Vessels 15: 26–32, 1978.
 39. Edman, K. A. P. The relation between sarcomere length and active tension in isolated semitendinosus fibres of the frog. J. Physiol. London 183: 407–417, 1966.
 40. Edman, K. A. P. Mechanical deactivation induced by active shortening in isolated muscle fibres of the frog. J. Physiol. London 246: 255–275, 1975.
 41. Fay, F. S. Mechanical properties of single isolated smooth muscle cells. In: Smooth Muscle Pharmacology and Physiology, edited by M. Worcel and G. Vassort. Paris: Inst. Natl. Santé Recherche Médicale, 1976, p. 327–340.
 42. Fay, F. S. Isometric contractile properties of single isolated smooth muscle cells. Nature 265: 553–556, 1977.
 43. Fay, F. S., P. H. Cooke, and P. G. Canaday. Contractile properties of isolated smooth muscle cells. In: Physiology of Smooth Muscle, edited by E. Bülbring and M. F. Shuba. New York: Raven, 1976, p. 249–265.
 44. Fay, F. S., and C. M. Delise. Contraction of isolated smooth‐muscle cells—structural changes. Proc. Natl. Acad. Sci. US. 70: 641–645, 1973.
 45. Fischer, H. Über die funktionelle Bedeutung des Spiralverlaufes der Muskulatur in der Arterienwand. Morphologisches Jahrbuch. 91: 394–445, 1951.
 46. Fisher, B. A., and R. M. Bagby. Reorientation of myofilaments during contraction of a vertebrate smooth muscle. Am. J. Physiol. 232: C5–C14, 1977 or
 47. Am. J. Physiol.: Cell Physiol. 1: C5–C14, 1977.
 48. Fung, Y‐C. B. Stress‐strain‐history relations of soft tissues in simple elongation. In: Biomechanics: Its Foundations and Objectives, edited by Y‐C. B. Fung, N. Perrone, and M. Anliker. Englewood Cliffs, NJ: Prentice‐Hall, 1972, chapt. 7, p. 181–208.
 49. Gabella, G. The force generated by a visceral smooth muscle. J. Physiol. London 263: 199–213, 1976.
 50. Gabella, G. Structural changes in smooth muscle cells during isotonic contraction. Cell Tissue Res. 170: 187–201, 1976.
 51. Gordon, A. M., A. F. Huxley, and F. J. Julian. The variation in isometric tension with sarcomere length in vertebrate muscle fibres. J. Physiol. London 184: 170–192, 1966.
 52. Gordon, A. M., and E. B. Ridgway. Length‐dependent electromechanical coupling in single muscle fibers. J. Gen. Physiol. 68: 653–669, 1976.
 53. Gordon, A. R., and M. J. Siegman. Mechanical properties of smooth muscle. I. Length‐tension and force‐velocity relations. Am. J. Physiol. 221: 1243–1249, 1971.
 54. Gordon, A. R., and M. J. Siegman. Mechanical properties of smooth muscle. II. Active State. Am. J. Physiol. 221: 1250–1254, 1971.
 55. Greven, K., K. H. Rudolph, and B. Hohorst. Creep after loading in the relaxed and contracted smooth muscle (Taenia coli of the guinea pig) under various osmotic conditions. Pfluegers Arch. European J. Physiol. 362: 255–260, 1976.
 56. Hardung, V., and L. Laszt. Die Beziehung zwischen Last und Verkürzungsgeschwindigkeit beim Gefässmuskel. Angiologica 3: 100–113, 1966.
 57. Hellstrand, P., and B. Johansson. The force‐velocity relation in phasic contractions of venous smooth muscle. Acta Physiol. Scand. 93: 157–166, 1975.
 58. Herlihy, J. T., and R. A. Murphy. Length‐tension relationship of smooth muscle of the hog carotid artery. Circulation Res. 33: 275–283, 1973.
 59. Herlihy, J. T., and R. A. Murphy. Force‐velocity and series elastic characteristics of smooth muscle from the hog carotid artery. Circulation Res. 34: 461–466, 1974.
 60. Hill, A. V. The heat of shortening and the dynamic constants of muscle. Proc. Roy. Soc. London Ser. B 126: 136–195, 1938.
 61. Hill, A. V. Trails and Trials in Physiology. London: Arnold, 1965.
 62. Hill, A. V. First and Last Experiments in Muscle Mechanics. London: Cambridge Univ. Press, 1970.
 63. Hooker, C. S., P. J. Calkins, and J. H. Fleisch. On the measurement of vascular and respiratory smooth muscle responses in vitro. Blood Vessels 14: 1–11, 1977.
 64. Huddart, H. The Comparative Structure and Function of Muscle. New York: Pergamon, 1975. (Intern. Ser. Monographs on Pure and Applied Biology: Zoology Division.)
 65. Huxley, A. F., and R. M. Simmons. Proposed mechanism of force generation in striated muscle. Nature 233: 533–538, 1971.
 66. Huxley, A. F., and R. M. Simmons. Mechanical transients and the origin of muscular force. Cold Springs Harbor Symp. Quant. Biol. 37: 669–680, 1972.
 67. Jewell, B. R., and J. R. Blinks. Drugs and the mechanical properties of heart muscle. In: Annual Review of Pharmacology, edited by H. W. Elliott, R. George, and R. Okun. Palo Alto, CA: Ann. Rev., 1968, vol. 8, p. 113–130.
 68. Jewell, B. R., and D. R. Wilkie. An analysis of the mechanical components in frog's skeletal muscle. J. Physiol. London 143: 515–540, 1958.
 69. Johansson, B. Active state in the smooth muscle of the rat portal vein in relation to electrical activity and isometric force. Circulation Res. 32: 246–258, 1973.
 70. Johansson, B. Determinants of vascular reactivity. Federation Proc. 33: 121–126, 1974.
 71. Johansson, B. Mechanics of vascular smooth muscle contraction. Experientia 31: 1377–1386, 1975.
 72. Johansson, B., and P. Hellstrand. Isometric and isotonic relaxation in venous smooth muscle. Acta Physiol. Scand. 93: 167–174, 1975.
 73. Johansson, B., P. Hellstrand, and B. Uvelius. Responses of smooth muscle to quick load change studied at high time resolution. Blood Vessels 15: 65–82, 1978.
 74. Johansson, B., B. Ljung, T. Malmfors, and L. Olson. Prejunctional supersensitivity in the rat portal vein as related to its pattern of innervation. Acta Physiol. Scand. Suppl. 349: 5–16, 1970.
 75. Johansson, B., and S. Mellander. Static and dynamic components in the vascular myogenic response to passive changes in length as revealed by electrical and mechanical recordings from the rat portal vein. Circulation Res. 36: 76–83, 1975.
 76. Jones, A. W., and G. Karreman. Ion exchange properties of the canine carotid artery. Biophys. J. 9: 884–909, 1969.
 77. Joyce, G. C., and P. M. H. Rack. Isotonic lengthening and shortening movements of cat soleus muscle. J. Physiol. London 204: 475–491, 1969.
 78. Joyce, G. C., P. M. H. Rack, and D. R. Westbury. The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements. J. Physiol. London 204: 461–474, 1969.
 79. Julian, F. J. The effect of calcium on the force‐velocity relation of briefly glycerinated frog muscle fibres. J. Physiol. London 218: 117–145, 1971.
 80. Julian, F. J., and R. L. Moss. The concept of active state in striated muscle. Circulation Res. 38: 53–59, 1976.
 81. Julian, F. J., and M. R. Sollins. Regulation of force and speed of shortening in muscle contraction. Cold Springs Harbor Symp. Quant. Biol. 37: 635–646, 1972.
 82. Laszt, L. Über die Eigenschaften der Gefässmuskulatur mit besonderer Berücksichtigung der Kalium‐Wirkung. Arch. Kreislaufforsch. 32: 220–244, 1960.
 83. Laszt, L. On the physiology of vascular smooth muscle in different regions. In: Physiology and Pharmacology of Vascular Neuroeffector Systems, edited by J. A. Bevan, R. F. Furchgott, R. A. Maxwell, and A. P. Somlyo. Basel: Karger, 1971, p. 263–272.
 84. Lazarides, E., and B. D. Hubbard. Immunological characterization of the subunit of the 100 Å filaments from muscle cells. Proc. Natl. Acad. Sci. US 73: 4344–4348, 1976.
 85. Leonard, E., and S. J. Sarnoff. Effect of aramine‐induced smooth muscle contraction on length‐tension diagrams of venous strips. Circulation Res. 5: 169–174, 1957.
 86. Lundholm, L., and E. Mohme‐Lundholm. Length at inactivated contractile elements, length‐tension diagram, active state and tone of vascular smooth muscle. Acta Physiol. Scand. 68: 347–359, 1966.
 87. Lundvall, J. Tissue hyperosmolality as a mediator of vasodilation and transcapillary fluid flux in exercising skeletal muscle. Acta Physiol. Scand. Suppl. 379: 1–142, 1972.
 88. Meiss, R. A. Some mechanical properties of cat intestinal muscle. Am. J. Physiol. 220: 2000–2007, 1971.
 89. Mulvany, M. J., and W. Halpern. Mechanical properties of vascular smooth muscle cells in situ. Nature 260: 617–619, 1976.
 90. Murphy, R. A. Contractile system function in mammalian smooth muscle. Blood Vessels 13: 1–23, 1976.
 91. Murphy, R. A., and A. C. Beardsley. Mechanical properties of the cat soleus muscle in situ. Am. J. Physiol. 227: 1008–1013, 1974.
 92. Murphy, R. A., S. P. Driska, and D. M. Cohen. Variations in actin to myosin ratios and cellular force generation in vertebrate smooth muscles. In: Excitation‐Contraction Coupling in Smooth Muscle, edited by R. Casteels, T. Godfraind, and J. C. Rüegg. Amsterdam: Elsevier, 1977, p. 417–424.
 93. Murphy, R. A., J. T. Herlihy, and J. Megerman. Force generating capacity and contractile protein content of arterial smooth muscle. J. Gen. Physiol. 64: 691–705, 1974.
 94. Murphy, R. A., and C. L. Seidel. Chemomechanical transduction in vascular smooth muscle. In: Vascular Neuroeffector Mechanisms: Proceedings, edited by J. A. Bevan, G. Burnstock, B. Johansson, R. A. Maxwell, and O. A. Nedergaard. Basel: Karger, 1976, p. 47–57. (Symp. on Vascular Neuroeffector Mechanisms, 2nd Intern., Odense, July‐August, 1975.)
 95. Paul, R. J., E. Glück, and J. C. Rüegg. Cross bridge ATP utilization in arterial smooth muscle. Pfluegers Arch. European J. Physiol. 361: 297–299, 1976.
 96. Paul, R. J., and J. W. Peterson. Relation between length, isometric force, and O2 consumption rate in vascular smooth muscle. Am. J. Physiol. 228: 915–922, 1975.
 97. Peiper, U., R. Laven, and M. Ehl. Force velocity relationships in vascular smooth muscle. The influence of temperature. Pfluegers Arch. European J. Physiol. 356: 33–45, 1975.
 98. Peterson, J. W., and R. J. Paul. Effects of initial length and active shortening on vascular smooth muscle contractility. Am. J. Physiol. 227: 1019–1024, 1974.
 99. Peterson, J. W., R. J. Paul, and S. R. Caplan. Force‐velocity relation and series elasticity in vascular smooth muscle (Abstract). Biophys. J. 13: 320a, 1973.
 100. Peterson, L., R. E. Jensen, and J. Parnell. Mechanical properties of arteries in vivo. Circulation Res. 8: 622–639, 1960.
 101. Pittman, R. N., and B. R. Duling. Oxygen sensitivity of vascular smooth muscle. I. In vitro studies. Microvascular Res. 6: 202–211, 1973.
 102. Podolsky, R. J., and A. C. Nolan. Cross‐bridge properties derived from physiological studies of frog muscle fibers. In: Contractility of Muscle Cells and Related Processes, edited by R. J. Podolsky. Englewood Cliffs, NJ: Prentice‐Hall, 1971, p. 247–260.
 103. Podolsky, R. J., and L. E. Teichholz. The relation between calcium and contraction kinetics in skinned muscle fibres. J. Physiol. London 211: 19–35, 1970.
 104. Pringle, J. W. S. Models of muscle. Symp. Soc. Exptl. Biol. 14: 41–68, 1960.
 105. Prosser, C. L. Smooth muscle. In: Annual Review of Physiology, edited by E. Knobil, I. S. Edelman, and R. R. Sonnenschein. Palo Alto, CA: Ann. Rev., 1974, vol. 36, p. 503–535.
 106. Roach, M. R., and A. C. Burton. The reason for the shape of the distensibility curves of arteries. Can. J. Biochem. Physiol. 35: 681–690, 1957.
 107. Rosenbluth, J. Smooth muscle: an ultrastructural basis for the dynamics of its contraction. Science 148: 1337–1339, 1965.
 108. Rüdel, R., and S. R. Taylor. Striated muscle fibers: facilitation of contraction at short lengths by caffeine. Science 172: 387–388, 1971.
 109. Rüegg, J. C. Smooth muscle tone. Physiol. Rev. 51: 201–248, 1971.
 110. Schoenberg, M., and R. J. Podolsky. Length‐force relation of calcium activated muscle fibers. Science 176: 52–54, 1972.
 111. Seidel, C. L., and R. A. Murphy. Stress relaxation in hog carotid artery as related to contractile activity. Blood Vessels 13: 78–91, 1976.
 112. Shoenberg, C. F., and D. M. Needham. A study of the mechanism of contraction in vertebrate smooth muscle. Biol. Rev. 51: 53–104, 1976.
 113. Siegman, M. J., T. M. Butler, S. U. Mooers, and R. E. Davies. Calcium‐dependent resistance to stretch and stress relaxation in resting smooth muscles. Am. J. Physiol. 231: 1501–1508, 1976.
 114. Simmons, R. M., and B. R. Jewell. Mechanics and models of muscular contraction. In: Recent Advances in Physiology (9th ed. ), edited by R. J. Linden. Edinburgh: Churchill Livingstone, 1974, p. 87–147.
 115. Small, J. V. The contractile apparatus of the smooth muscle cell: structure and composition. In: The Biochemistry of Smooth Muscle, edited by N. L. Stephens. Baltimore: Univ. Park, 1977, p. 379–411.
 116. Small, J. V., and A. Sobieszek. Studies on the function and composition of the 10‐NM (100‐A) filaments of vertebrate smooth muscle. J. Cell Sci. 23: 243–268, 1977.
 117. Somlyo, A. P., and A. V. Somlyo. Vascular smooth muscle. I. Normal structure, pathology, biochemistry, and biophysics. Pharmacol. Rev. 20: 197–272, 1968.
 118. Sonnenblick, E. H. Implications of muscle mechanics in the heart. Federation Proc. 21: 975–990, 1962.
 119. Sparks, H. V.Jr. Effect of quick stretch on isolated vascular smooth muscle. Circulation Res. 15: (Suppl. 1) I‐254–I‐260, 1964.
 120. Speden, R. N. Excitation of vascular smooth muscle. In: Smooth Muscle, edited by E. Bülbring, A. F. Brading, A. W. Jones, and T. Tomita. Baltimore: Williams & Wilkins, 1970, p. 558–588.
 121. Stephens, N. L. Effect of hypoxia on contractile and series elastic components of smooth muscle. Am. J. Physiol. 224: 318–321, 1973.
 122. Stephens, N. L. Physical properties of contractile systems. In: Methods in Pharmacology. Smooth Muscle, edited by E. E. Daniel and D. M. Paton. New York: Plenum, 1975, vol. 3, chapt. 13, p. 265–296.
 123. Stephens, N. L., and B. S. Chiu. Mechanical properties of tracheal smooth muscle and effects of O2, CO2, and pH. Am. J. Physiol. 219: 1001–1008, 1970.
 124. Strong, K. C. A study of the structure of the media of the distributing arteries by the method of microdissection. Anat. Record 72: 151–162, 1938.
 125. Sugi, H. Tension changes during and after stretch in frog muscle fibres. J. Physiol. London 227: 237–253, 1972.
 126. Taylor, S. R., and R. Rüdel. Striated muscle fibers: inactivation of contraction induced by shortening. Science 167: 882–884, 1970.
 127. Thames, M. C., L. E. Teichholz, and R. J. Podolsky. Ionic strength and the contraction kinetics of skinned muscle fibers. J. Gen. Physiol. 63: 509–530, 1974.
 128. Tuma, J. J. Technology Mathematics Handbook. New York: McGraw‐Hill, 1975.
 129. Twarog, B. M. Aspects of smooth muscle function in molluscan catch muscle. Physiol. Rev. 56: 829–838, 1976.
 130. Uvelius, B. Isometric and isotonic length‐tension relations and variations in cell length in longitudinal smooth muscle from rabbit urinary bladder. Acta Physiol. Scand. 97: 1–12, 1976.
 131. White, D. C. S., and J. Thorson. The kinetics of muscle contraction. In: Progress in Biophysics and Molecular Biology, edited by J. A. V. Butler. and D. Noble. Oxford: Pergamon, 1973, vol. 27, p. 173–255.
 132. Wise, R. M., J. F. Rondinone, and F. N. Briggs. Effect of calcium on force‐velocity characteristics of glycerinated skeletal muscle. Am. J. Physiol. 221: 973–979, 1971.
 133. Woledge, R. C. The energetics of tortoise muscle. J. Physiol. London 197: 685–707, 1968.
 134. Wolinsky, H., and M. M. Daly. A method for the isolation of intima‐media samples from arteries. Proc. Soc. Exptl. Biol. Med. 135: 364–368, 1970.
 135. Zatzman, M., R. W. Stacy, J. Randall, and A. Eberstein. Time course of stress relaxation in isolated arterial segments. Am. J. Physiol. 177: 299–302, 1954.

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Article Title: Mechanics of Vascular Smooth Muscle
 

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R. A. Murphy. Mechanics of Vascular Smooth Muscle. Compr Physiol 2011, Supplement 7: Handbook of Physiology, The Cardiovascular System, Vascular Smooth Muscle: 325-351. First published in print 1980. doi: 10.1002/cphy.cp020213