Basic Research in Cardiology A r c h i v fiir K r e i s l a u f f o r s c h u n g O f f i c i a l J o u r n a l of t h e G e r m a n A s s o c i a t i o n of C a r d i o v a s c u l a r R e s e a r c h E d i t e d b y R. J a c o b ,
V o l u m e 74
T i i b i n g e n , a n d W. S c h a p e r ,
January/February
Bad Nauheim
Number 1
EDITORIAL Basic Res. Cardiol. 74, 1-9 (1979) 9 1979 Dr. Dietdch Steinkopff Verlag, Darmstadt ISSN 0300-8428
Bockus Institute, Graduate Hospital, and Department of Physiology, University of Pennsylvania, Philadelphia (USA)
C e n t r i b u t i e n ef s m e e t h m u s c l e te a r t e r i a l w a l l mechanics*) Beitrag der glatten Muskulatur zur M e c h a n i k der Arterienwand R . H. C o x With 4 figures (Received October 25, 1978)
Summary The contribution of vascular smooth muscle to the mechanical properties of arteries can be quantitated using elastomeric and classical muscle concepts. Such analyses can be performed using pressure-diameter data obtained from a given specimen u n d e r conditions of active and passive muscle. The elastomeric approach represents arterial wall mechanics in terms of incremental elastic moduli and theoretical characteristic impedance, z 0. Activation of muscle produces a reduction in values of incremental m o d u lu s at almost all values of transmural pressure. Values of Z 0 are increased at low pressure and decreased at high pressure following activation of muscle. In the muscle approach, the mechanics of arteries are quantitated in terms of active stress d e v e l o p m e n t and constriction responses as a function of muscle length and pressure, respectively. Active stress-muscle length and shortening-load relations obtained from arterial smooth muscle are qualitatively similar to those of other types of muscles. The length and load dependencies of these relations are what one would expect based on a sliding filament arrangement of contractile filaments. *) The research described herein from the author's laboratory was supported in part by Grant HL-17840 from U.S.P.H.S. 783
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Basic Research in Cardiology, Vol. 74, No. 1 (1979)
Experimental methods have also been developed to study the properties of series elastic (SE) elements in these preparations. Load-extension relations of the SE are dependent on muscle length and anatomical site of the sample. With increasing muscle length, the SE appears to become stiffer. SE properties vary greatly in different preparations with a close correlation between SE stiffness and the maximum value of active force developed by the preparation. Neither of Hlll's three element models appear to be directly applicable in representing arterial SE, and its morphological basis is unclear. B l o o d vessels in the arterial circulation serve a n u m b e r of different functions. L a r g e arteries act as elastic reservoirs storing a p o r t i o n of the b l o o d ejected d u r i n g each heart beat (1). Small arteries in the circulation r e p r e s e n t the region w h e r e arterial p r e s s u r e a n d b l o o d flow d i s t r i b u t i o n are controlled b y n e u r o h u m o r a l m e c h a n i s m s (2). In addition, the wall of a n u m b e r of large to m e d i u m size arteries c o n t a i n specialized n e r v e e n d i n g s w h i c h act as " b a r o r e c e p t o r s " g e n e r a t i n g afferent nerve activity w h i c h is utilized b y the central n e r v o u s s y s t e m in the control of the circulation (3). The arterial s y s t e m m e e t s c h a n g e s in the short t e r m d e m a n d s of the o r g a n i s m t h r o u g h variations in the degree of activation of its v a s c u l a r s m o o t h muscle. I n q u a n t i t a t i n g the c o n t r i b u t i o n of v a s c u l a r s m o o t h m u s cle activity to the f u n c t i o n a l properties of arteries, two separate a p p r o a c h e s have b e e n developed. The first a p p r o a c h a t t e m p t s to define the effects of s m o o t h m u s c l e activation in t e r m s of its effect o n elastic properties a n d h e m o d y n a m i c p a r a m e t e r s of the circulation; this is the elastomeric a p p r o a c h (4-12). The s e c o n d a p p r o a c h a t t e m p t s to define the effects of activation in t e r m s of isometric force d e v e l o p m e n t a n d isotonic or isobaric shortening; this is the classical m u s c l e a p p r o a c h (8-14). The elastomeric a p p r o a c h is p r o b a b l y m o r e a p p r o p r i a t e l y applied to large arteries in the circulation, while the m u s c l e a p p r o a c h is p r o b a b l y m o r e applicable to the small arteries (the resistance vessels) in the circulation. While these two a p p r o a c h e s define the same p h y s i c a l / c h e m i c a l processes in the arterial s m o o t h muscle, a one-to-one c o r r e s p o n d e n c e b e t w e e n these r e p r e s e n t a t i o n s m a y n o t necessarily be expected. As b o t h of these a p p r o a c h e s are i m p o r t a n t to our u n d e r s t a n d i n g of the physiological function of the arterial wall, m e t h o d s h a v e b e e n d e v e l o p e d over the past few y e a r s to define the effects of activation of v a s c u l a r s m o o t h m u s c l e on arterial wall properties in t e r m s of b o t h a p p r o a c h e s u s i n g intact, isolated vascular s e g m e n t s (4-14). This brief d i s c u s s i o n will a t t e m p t to s u m m a r i z e s o m e of these results a n d indicates future areas of study. A detailed d e s c r i p t i o n of the m e t h o d s e m p l o y e d in the studies to be d e s c r i b e d is b e y o n d the s c o p e of this report. R e a d e r s are directed to the original studies (4-16). E x p e r i m e n t a l data are usually o b t a i n e d as p r e s s u r e - d i a m e t e r relations u n d e r c o n d i t i o n s of active a n d passive s m o o t h muscle. The f o r m e r is usually a c h i e v e d with m a x i m a l activation b y epinephrine, n o r e p i n e p h r i n e , p o t a s s i u m or the like. Passive c o n d i t i o n s are obtained u s i n g a variety of c h e m i c a l or m e c h a n i c a l means. P r e s s u r e / d i a m e t e r relations r e c o r d e d u n d e r c o n d i t i o n s of active a n d passive s m o o t h m u s c l e are used to q u a n t i t a t e the c o n t r i b u t i o n of s m o o t h m u s c l e to arterial wall p r o p e r t i e s u s i n g the two a p p r o a c h e s . I n t h e case of the classical m u s c l e a p p r o a c h these p r e s s u r e / d i a m e t e r data are u s e d to
Cox, ContributJon of smooth muscle
3
d e t e r m i n e v a l u e s of a c t i v e w a l l s t r e s s a n d a c t i v e d i a m e t e r r e s p o n s e as d e f i n e d in f i g u r e 1. T h e a c t i v e d i a m e t e r r e s p o n s e is o b t a i n e d as t h e d i f f e r e n c e in a r t e r i a l d i a m e t e r u n d e r a c t i v e a n d p a s s i v e c o n d i t i o n s at a g i v e n v a l u e of t r a n s m u r a l p r e s s u r e . T h e s e d i a m e t e r d i f f e r e n c e s m a y b e n o r m a l i z e d b y d i v i d i n g b y t h e p a s s i v e d i a m e t e r at e a c h p r e s s u r e level. A c t i v e s t r e s s r e s p o n s e s are q u a n t i t a t e d f r o m t h e d i f f e r e n c e in v a l u e s of w a l l s t r e s s u n d e r a c t i v e a n d p a s s i v e c o n d i t i o n s at a g i v e n v a l u e of b l o o d v e s s e l d i a m e t e r . V a l u e s of w a l l s t r e s s (ae) a r e d e t e r m i n e d f r o m p r e s s u r e ( P ) - d i a m e t e r d a t a u s i n g t h e f o l l o w i n g e q u a t i o n (17): a oe = ~
P
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w h e r e a a n d b r e p r e s e n t t h e v a l u e of i n t e r n a l a n d e x t e r n a l radii, r e s p e c tively, at e a c h p r e s s u r e level. I n t h e e l a s t o m e r i c a p p r o a c h , t h e effects of s m o o t h m u s c l e a c t i v a t i o n are q u a n t i t a t e d in t e r m s of t w o v a r i a b l e s : t h e i n c r e m e n t a l e l a s t i c m o d u l u s and the characteristic impedance. The incremental elastic m o d u l u s repres e n t s t h e s l o p e of t h e t a n g e n t i a l s t r e s s - s t r a i n curve, a n d is c o m p u t e d u s i n g an e q u a t i o n of t h e s o r t (17): 2a2b AP E = -b2 a-------_ ~ Ab (2) V a l u e s of t h e o r e t i c a l c h a r a c t e r i s t i c i m p e d a n c e r e p r e s e n t t h e h i g h freq u e n c y a s y m p t o t e a b o u t w h i c h v a l u e s of v a s c u l a r i m p e d a n c e o s c i l l a t e (24), a n d r e p r e s e n t s t h e ratio of p u l s a t i l e p r e s s u r e a n d flow. It is d e t e r m i n e d p r i m a r i l y b y t h e e l a s t i c a n d g e o m e t r i c p r o p e r t i e s of t h e b l o o d
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Fig. 1. Schematic summary of methods used in the representation of the active mechanics of arterial smooth muscle. A: Pressure-diameter relations obtained under conditions of active (left curve) and passive (right curve) smooth muscle. Isometric stress response and isobaric diameter response are defined in the diagram. Examples of values of isometric stress response at different values of norrealized diameter (panel B) and isobaric diameter response at different values of transmural pressure (panel C) are also shown.
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Basic Research in Cardiology, Vol. 74, No. 1 (1979)
v e s s e l s e g m e n t c l o s e to t h e m e a s u r e m e n t site, a n d d e t e r m i n e d f r o m t h e f o l l o w i n g e q u a t i o n (17): 1 ~/s (b 2 - a 2) ~ f ~ - ~ ~_-~ (3) Z0 ~a-----w h e r e s is t h e d e n s i t y of b l o o d . I n t h e left p a n e l of f i g u r e 2, t h e effects of s m o o t h m u s c l e a c t i v a t i o n on i n c r e m e n t a l e l a s t i c m o d u l u s of c a n i n e iliac a r t e r i e s a r e s h o w n . A c t i v a t i o n p r o d u c e s a r e d u c t i o n in v a l u e s of i n c r e m e n t a l e l a s t i c m o d u l u s at s p e c i f i c v a l u e s of t r a n s m u r a l p r e s s u r e (8). T h e m a g n i t u d e of t h i s r e d u c t i o n v a r i e s q u i t e c o n s i d e r a b l y at d i f f e r e n t t r a n s m u r a l p r e s s u r e s a n d in d i f f e r e n t s p e c i m e n s (8-12), a n d c a n be c o n s i d e r e d to b e a m e a s u r e of s m o o t h m u s c l e contractility. T h e v a r i a t i o n s of c h a r a c t e r i s t i c i m p e d a n c e w i t h t r a n s m u r a l p r e s s u r e is g i v e n in t h e r i g h t p a n e l of f i g u r e 2. U n d e r p a s s i v e c o n d i t i o n s , c h a r a c t e r i s tic i m p e d a n c e u s u a l l y i n c r e a s e s in a m o n o t o n i c f a s h i o n w i t h t r a n s m u r a l p r e s s u r e . U n d e r a c t i v a t e d c o n d i t i o n s , t h e r e is a m i n i m u m v a l u e of c h a r a c t e r i s t i c i m p e d a n c e at a p p r o x i m a t e l y 120 m m Hg. A t p r e s s u r e s a b o v e a n d below this value, characteristic i m p e d a n c e increases. S o m e vessels from s o m e s p e c i e s s h o w a d i f f e r e n t k i n d of b e h a v i o r u n d e r c o n d i t i o n s of p a s s i v e s m o o t h m u s c l e (8, 11). T h i s " U - s h a p e d " v a r i a t i o n of c h a r a c t e r i s t i c i m p e d a n c e w i t h t r a n s m u r a l p r e s s u r e is a g e n e r a l c h a r a c t e r i s t i c of all a r t e r i e s w i t h a c t i v a t e d m u s c l e . I t is i n t e r e s t i n g t h a t all v e s s e l s s t u d i e d a p p e a r to p o s s e s s a m i n i m u m v a l u e of c h a r a c t e r i s t i c i m p e d a n c e at a t r a n s m u r a l p r e s s u r e w i t h i n t h e a n i m a l ' s n o r m a l p h y s i o l o g i c a l r a n g e . It w o u l d be of i n t e r e s t to a s c e r t a i n if a c a u s a l r e l a t i o n e x i s t s b e t w e e n t h i s m i n i m u m a n d t h e n o r m a l v a l u e of a r t e r i a l p r e s s u r e i n a n a n i m a l . T h e d a t a s h o w n in f i g u r e 3 a r e r e p r e s e n t a t i v e of t h e a c t i v e m e c h a n i c a l p r o p e r t i e s of a r t e r i a l s m o o t h m u s c l e (4, 5, 8-13). T h e a c t i v e s t r e s s r e s p o n s e i n c r e a s e s n e a r l y l i n e a r l y in m a g n i t u d e to a m a x i m u m at s o m e o p t i m u m l e n g t h ( L ~ ) . F u r t h e r i n c r e a s e s in l e n g t h r e s u l t in a d e c r e a s e in t h e a c t i v e stress response. Such a relation b e t w e e n active force d e v e l o p m e n t and
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Fig. 2. Effects of smooth muscle activation on the variation of incremental elastic modulus and characteristic impedance with transmura] pressure. Data were obtained from a series of 12 canine renal arteries under conditions of active (closed squares) and passive (open circles) smooth muscle. Symbols are means while vertical bars are _+ 1 SEM.
Cox, Contribution of smooth muscle
5
m u s c l e l e n g t h is similar to that of o t h e r t y p e s of muscle, a n d s u g g e s t s a sliding filament t y p e a r r a n g e m e n t of the contractile a p p a r a t u s (18, 19). T h e active d i a m e t e r r e s p o n s e exhibits a similar variation with t r a n s m u r a l pressure. That is, a m a x i m u m value for this q u a n t i t y exists at p r e s s u r e s in the range of 50-150 m m H g . Substantial differences exist in t h e s e two m e a s u r e s of arterial s m o o t h m u s c l e f u n c t i o n related to age (6, 8, 9, 20), a n d a n a t o m i c a l location (10, 12) a m o n g other factors. The results given in these t w o figures s u m m a r i z e s the m a n n e r in w h i c h the c o n t r i b u t i o n of s m o o t h m u s c l e to arterial wall m e c h a n i c s can be q u a n t i t a t e d b y the two a p p r o a c h e s . This analysis also lends itself to the d e t e r m i n a t i o n of quantitative c h a n g e s or differences in the c o n t r i b u t i o n of s m o o t h m u s c l e to the m e c h a n i c a l properties of arteries. This, in fact, h a d b e e n d o n e in a n u m b e r of instances (8-12). I n general, the results indicate that the two different a p p r o a c h e s as well as the individual variables do n o t always yield the same conclusion. F o r example, a detailed c o m p a r i s o n of these responses have b e e n m a d e u s i n g carotid arteries from rat, rabbit, a n d dog (11). T h e m a x i m u m active stress r e s p o n s e was the s a m e in carotids f r o m rabbit a n d d o g a n d b o t h were larger t h a n that of the rat carotid. However, the m a x i m u m d i a m e t e r r e s p o n s e was largest in r a b b i t carotids while that of d o g and rat carotids were the same. Thus, the m a x i m u m d i a m e t e r r e s p o n s e for the rabbit carotids was larger t h a n that of the dog carotids in spite of the fact that t h e y p r o d u c e d the s a m e m a x i m u m stress response. T h e m a x i m u m d i a m e t e r r e s p o n s e was the same in d o g a n d rat carotids in spite of the fact that the rat carotids h a d a smaller m a x i m u m active stress r e s p o n s e c o m p a r e d to the d o g carotids. T h e decrease in i n c r e m e n t a l m o d u l u s with activation was the same in dog a n d rat carotids while b o t h were smaller t h a n that of the rabbit carotids. These differences were similar to the relative differences in d i a m e t e r responses. On the o t h e r hand, the effects of activation on the variations of Z0 w e r e largest in the rabbit carotids, and smallest in the d o g carotids with the rat carotids b e i n g intermediate. 3
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Fig. 3. Effects of smooth muscle activation analyzed by the muscle approach. The left panel shows the variation of isometric stress response as a function of normalized diameter. The right panel shows the variation of isobaric diameter response with transmural pressure. Symbols represent means, while horizontal and vertical bars are • 1 SEM for data averaged from 12 canine renal arteries.
6
Basic Research in Cardiology, Vol. 74, No. 1 (1979)
In other studies, arteries which exhibit larger stress responses produce l a r g e r (11, 21, 22) or t h e s a m e (8, 10, 11, 21) d i a m e t e r r e s p o n s e c o m p a r e d to a n o t h e r a r t e r y . Also, a r t e r i e s p r o d u c i n g t h e s a m e a c t i v e s t r e s s r e s p o n s e g e n e r a t e t h e s a m e (22) or a l a r g e r (11) d i a m e t e r r e s p o n s e . Thus, a c l e a r r e l a t i o n d o e s n o t a l w a y s e x i s t b e t w e e n t h e s e t w o m e a s u r e s of m u s c l e in d i f f e r e n t arteries. L i k e w i s e , t h e c o n t r i b u t i o n of s m o o t h m u s c l e in t h e e l a s t o m e r i c a p p r o a c h c a n p r o d u c e t h e s a m e c o n c l u s i o n s as d e t e r m i n e d w h e n a c t i v e d i a m e t e r r e s p o n s e s are e m p l o y e d (11, 21, 22) or w h e n a c t i v e s t r e s s r e s p o n s e s a r e e m p l o y e d (8, 10). I n o t h e r cases, d i f f e r e n t c o n c l u s i o n s c a n be r e a c h e d . O b v i o u s l y , no c l e a r r e l a t i o n e x i s t s b e t w e e n t h e s e v a r i o u s m e a s u r e s of t h e c o n t r i b u t i o n of s m o o t h m u s c l e a c t i v a t i o n to a r t e r i a l m e c h a n i c s e i t h e r b e t w e e n or w i t h i n t h e t w o a p p r o a c h e s . N u m e r o u s a d d i t i o n a l f a c t o r s c a n be i d e n t i f i e d t h a t c o u l d b e r e s p o n s i b l e for t h i s l a c k of u n a n i m i t y , s u c h as t h e p r e s e n c e of p a s s i v e t i s s u e e l e m e n t s c o u p l e d to t h e c o n t r a c t i l e a p p a r a t u s , t h e o r g a n i z a t i o n of t h e c o n t r a c t i l e a p p a r a t u s , i n t e r c e l l u l a r c o u p l i n g , o r g a n i z a t i o n of c o n t r a c t i l e u n i t s , t i s s u e c o m p r e s s i o n , w a l l t h i c k n e s s , etc. Clearly, t h e c o n t r i b u t i o n of s m o o t h m u s c l e to a r t e r i a l w a l l p r o p e r t i e s m u s t b e a s s e s s e d in t e r m s of s p e c i f i c v a r i a b l e s w i t h t h e k n o w l e d g e t h a t a g i v e n c o n c l u s i o n m a y n o t a p p l y if o t h e r v a r i a b l e s a r e c o n s i d e r e d . F u r t h e r m o r e , it is also c l e a r t h a t a d d i t i o n a l s t u d i e s m u s t b e u n d e r t a k e n to d e f i n e t h e f a c t o r s w h i c h d e t e r m i n e t h e s e i n t e r r e l a t i o n s in more quantitative terms. S i m i l a r to s t r i a t e d m u s c l e , a r t e r i a l s m o o t h m u s c l e b e h a v e s m e c h a n i c a l l y as if a p a s s i v e e l a s t i c s t r u c t u r e w e r e f u n c t i o n a l l y c o n n e c t e d in s e r i e s w i t h t h e c o n t r a c t i l e a p p a r a t u s (series elasticity). T h e p r e s e n c e of a subs t a n t i a l a m o u n t of s e r i e s e l a s t i c i t y in a r t e r i a l s m o o t h m u s c l e p r e p a r a t i o n s s u g g e s t s t h a t t h e s e p a s s i v e e l a s t i c s t r u c t u r e s h a v e c a p a c i t y to m o d i f y t h e e x p r e s s i o n of t h e i n t r i n s i c c h a r a c t e r i s t i c s of t h e m u s c l e c o n t r a c t i l e ele-
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Fig. 4. A summary of some mechanical properties of series elastic elements in arterial smooth muscle. The left panel shows the variation of canine iliac artery SE properties as a function of initial muscle length, and the right panel shows data from a number of arterial sites at a muscle length equivalent to Lmax-Symbols are identified in the inserts and represent means while bars represent _+ 1 SEM.
Cox, Contribution of smooth muscle
7
m e n t s m a n i f e s t as arterial wall r e s p o n s e s (12). It is p o s s i b l e to d e t e r m i n e t h e p r o p e r t i e s of t h e s e series elastic e l e m e n t s (SE) e x p e r i m e n t a l l y b y several different m e t h o d s . One of t h e characteristics of arterial s m o o t h m u s c l e is a v a r i a t i o n of series elasticity w i t h m u s c l e length (23). T h e left p a n e l of figure 4 s h o w s s u c h a v a r i a t i o n in iliac artery s m o o t h m u s c l e at six different v a l u e s of initial m u s c l e length. If the "Voigt m o d e l " of Hill c o u l d b e u s e d to r e p r e s e n t arterial s m o o t h m u s c l e all of t h e s e c u r v e s for different m u s c l e lengths w o u l d fall a l o n g a single u n i q u e curve. Since t h e y do not, it is c o n c l u d e d t h a t a Voigt t y p e of m o d e l is not a p p l i c a b l e to this p r e p a r a t i o n . If a " M a x w e l l m o d e l " w e r e applicable, t h e s e c u r v e s w o u l d all b e s u p e r i m p o s a b l e if t r a n s l a t e d to the origin of this graph, t h a t is, t h e y w o u l d h a v e t h e s a m e slopes. Since t h e y do not, it a p p e a r s t h a t a M a x w e l l t y p e of m o d e l is not a p p l i c a b l e either. This m e a n s t h a t a different f o r m of m o d e l m u s t b e d e v e l o p e d to r e p r e s e n t arterial s m o o t h m u s c l e . T h e d e v e l o p m e n t of s u c h a m o d e l is n e c e s s a r y for d e t e r m i n i n g t h e t r u e p r o p e r t i e s of t h e contractile a p p a r a t u s of v a s c u l a r s m o o t h m u s c l e a n d r e p r e s e n t s a n o t h e r f u t u r e a r e a for study. T h e p r o p e r t i e s of the SE in arterial s m o o t h m u s c l e also d e m o n s t r a t e a m a r k e d a n a t o m i c a l v a r i a t i o n (12). Results of e x p e r i m e n t s o n six different arterial sites are s u m m a r i z e d in the right p a n e l of figure 4. T h e s e m e a s u r e m e n t s of SE w e r e m a d e at a m u s c l e l e n g t h c o r r e s p o n d i n g to Lmax,i. e., t h e o p t i m u m length for active stress d e v e l o p m e n t in t h e s e p r e p a r a t i o n s . It is o b v i o u s t h a t a w i d e v a r i a t i o n in SE p r o p e r t i e s e x i s t at t h e s e different arterial sites, w i t h v a l u e s for t h e carotid a n d i n t e r n a l t h o r a c i c b e i n g t h e m o s t c o m p l i a n t a n d values f r o m t h e c o r o n a r y a n d m e s e n t e r i c arteries b e i n g the stiffest. I t is c o n c e i v a b l e t h a t a p o r t i o n of t h e s e d i f f e r e n c e s in SE m e c h a n i c a l p r o p e r t i e s is t h e result of d i f f e r e n c e s in t h e rest l e n g t h of SE in these preparations. E x p e r i m e n t a l e v i d e n c e exists to s u g g e s t t h a t t h e m a j o r p o r t i o n of SE in arterial s m o o t h m u s c l e resides outside of the contractile s y s t e m (15, 24). One p o t e n t i a l c a n d i d a t e for a m o r p h o l o g i c a l site for S E in arterial s m o o t h m u s c l e is the c o n n e c t i v e tissue m a t r i x t h a t c o u p l e s i n d i v i d u a l s m o o t h m u s c l e cells. Studies of b l o o d vessel m o r p h o l o g y indicate t h a t b o t h collag e n a n d elastin e x i s t in the m e d i a of large to small sized arteries (25-27). It is possible, therefore, t h a t t h e relative c o n t e n t of collagen a n d elastin m a y correlate w i t h t h e m e c h a n i c a l p r o p e r t i e s of the SE. H o w e v e r , e x p e r i m e n tal studies indicate t h a t no clear relation exists b e t w e e n c o n n e c t i v e tissue c o m p o s i t i o n of arteries a n d the m e c h a n i c a l p r o p e r t i e s of t h e i r SE. Obviously, t h e t r u e situation (i. e., the m o r p h o l o g i c a l basis for SE in arterial s m o o t h m u s c l e ) is m o r e c o m p l i c a t e d t h a n s i m p l y t h e relative a m o u n t of collagen a n d elastin in t h e b l o o d vessel. T h e identification of this basis for the SE is an i m p o r t a n t direction for s t u d y a n d m a y p r o v i d e i m p o r t a n t insight into t h e m e c h a n i s m of c o n t r a c t i o n a n d force t r a n s d u c t i o n . As i n d i c a t e d b y t h e m a g n i t u d e of the SE in t h e s e v a r i o u s arterial s m o o t h m u s c l e s , the p o t e n t i a l for a s u b s t a n t i a l distortion of the intrinsic p r o p e r ties of the contractile a p p a r a t u s is present.
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Basic Research in Cardiology, Vol. 74, No. 1 (1979)
Zusammenfassung D e r Beitrag der glatten Muskulatur zu den meehanischen Eigenschaften der A_rterien kann auf der Grundlage zweier Muskelkonzepte quantifiziert werden, n~mlich der Elastizit~tslehre und des klassischen Konzepts. Derartige Analysen k6nnen unter V e r w e n d u n g der Daten von Druck und Durchmesser v o r g e n o m m e n werden, die m a n yon einem einzelnen Versuehsobjekt unter den Bedingungen der R u h e oder der Aktivit~t des Muskels erh~it. Das elastische Konzept beschreibt die Mechanik der Arterienwand in F o r m des tangentiellen elastischen Moduls und der charakteristischen Impedanz, Z o, Die Muskelaktivierung bewirkt eine A b n a h m e des tangentiellen Moduls bei fast allen transmuralen Druckwerten. Die Werte yon Z 0 steigen nach Aktivierung des Muskels bei niederen Drucken und n e h m e n bei hohen Drucken ab. B e i m klassischen Muskelkonzept wird die Mechanik der Arterien quantiflziert als aktive Spannungsentwicklung und Konstriktion als Funktion yon Muskell~nge oder Druck. Die aktiven L~ngen-Spannungs-Beziehungen und die Beziehung zwischen Verkfirzung und Last, die m a n von arteriellen glatten Muskeln erh~It, sind qualitativ ~hnlich wie bei anderen Muskeltypen. Die LAngenund Lastabh~/Igigkeit dieser Beziehungen sind so, wie m a n sie aufgrund des Gleitmodells der kontraktilen Filamente erwarten wfirde. Es wurden auch experimentelle Methoden entwickelt, u m die Eigenschaften des serienelastischen Elements an diesen Pr~paraten zu untersuchen. Die Beziehungen zwischen Last und Verl~ngerung des serienelastischen Elements h~ingen yon der Muskell~nge und der anatomischen Herkunft des PrAparates ab. Mit wachsender Niuskell~nge scheint das serienelastische Element steiferzu werden. Die serienelastischen Eigenschaften variierten stark bei verschiedenen Pr~parationen m i t einer e n g e n Korrelation zwischen der Steifheit des serienelastischen Elements u n d d e m m ax i m al en Wert der aktiven Kraftentwicklung des Pr~parates. Keines der DreiElementen-Modelle yon Hill scheint fiir die Beschreibung der Serienelastizit~it direkt an wen d b a r zu sein. Seine morphologische Grundlage ist unklar.
References 1. Mllnor, W. R.: Arterial im p e d a n c e as ventricular afterload. Circulation Res. 36, 565-570 (1975). 2. Ab b o u d , F. M.: Control of the various components of the peripheral vasculature. Fed. Proc. 31, 1226-1239 (1972). 3. Kirchheim, H. R.: Systemic arterial baroreceptor reflexes. Physiol. Rev. 56, 100-176 (1976). 4. Speden, 17. iV.: The m a i n t e n a n c e of arterial constriction at different transmural pressures. J. Physiol. 229, 361-381 (1973). 5. Dobrln, P. B., A. A. Rovick: Influence of vascular smooth muscle on contractile mechanics and elasticity of arteries. Am. J. Physiol. 217, 1644-1651 (1969). 6. Berry, C. L., S. E. Greenwald, J. F. Rivett: Static mechanical properties of the developing and mature rat aorta. Cardiovascular Res. 9, 669-678 (1975). 7. Busse, R., R. D. Bauer, Y. S u m m a , H. K 6 m e r , Th. Pasch: Comparison of the viseo-elastic properties of the tail artery in spontaneously hypertensive and n o r m o t e n s i v e rats. Pflfigers Arch. 364, 175-181 (1976). 8. Cox, R. H.: Effects of age on the mechanical properties of rat carotid artery. Am. J. Physiol. 233, H256-H263 (1977). 9. Cox, R. H., A. W. Jones, 1VI. L. Swain: Mechanics and electrolyte composition of arterial s m o o t h muscle in developing dogs. Am. J. Physiol. 231, 77-83 (1976). 10. Cox, R. H.: Arterial wall mechanics and composition and the effects of smooth muscle activation. Am. J. Physiol. 229, 807-812 (1975). 11. Cox, R. H.: Comparison of carotid artery mechanics in the rat, rabbit, and dog. Am. J. Physiol. 234, H280-H288 (1978).
Cox, Contribution of smooth muscle
9
12. Cox, R. H.: Regional variation of series elasticity in canine arterial smooth muscles. Am. J. Physiol. 234, H542-H551 (1978). 13. Dobrin, P. B.: Isometric and isobaric contraction of carotid arterial smooth muscle. Am. J. Physiol. 225, 659-663 (1973). 14. Dobrin, P. B.: Vascular muscle series elastic element stiffness during isometric contraction. Circulation Res. 34, 242-250 (1974). 15. Cox, R. H.: Determination of series elasticity in arterial smooth muscle. Am. J. Physiol. 233, H248-H255 (1977). 16. Cox, R. H.: Three-dimensional mechanics of arterial segments in vitro: methods. J. Applied Physiol. 36, 381-384 (1974). 17. Cox, R. H.: Effects of norepinephrine on mechanics of arteries in vitro. Am. J. Physiol. 231, 420-425 (1976). 18. Johansson, B.: Mechanics of vascular smooth muscle contraction. Experientia 31, 1377-1476 (1975). 19. Murphy, R. A.: Contractile system function in m a m m a l i a n smooth muscle. Blood Vessels 13, 1-23 (1976). 20. Speden, R. IV.: Muscle load and constriction of the rabbit ear artery. J. Physiol. 248, 531-553 (1975). 21. Cox, R. H.: Arterial wall mechanics and composition in normal and spontaneously hypertensive rats. Fed. Proc. 37, 349 (1978). 22. Cox, R. 1,I.: Alterations in active and passive mechanics of rat carotid artery associated with experimental hypertension. Am. J. Physiol. (1978). Submitted for publication. 23. Cox, R. H.: Influence of muscle length on series elasticity in arterial smooth muscle. Am. J. Physiol. 234, C146-C154 (1978). 24. Dobrin, P., T. Canfield: Identification of smooth muscle series elastic compon e n t in intact carotid artery. Am. J. Physiol. 232, H122-H130 (1977). 25. Pease, D. C., S. Molinari: Electron microscopy of muscular arteries; Pial vessels of the cat and monkey. J. Ultrastructure Res. 3, 447-468 (1960). 26. Clis W. J.: The aortic tunica media in aging rats. Experimental and Molecular Pathology 13, 172-189 (1970). 27. Cox, R. H.: The mechanism of force transduction between vascular smooth muscle cells. In, Third Int. Symp. Vascular Neuroeffector Mechanisms, Eds. J. A. Bevan, et al. (Basel 1979). Author's address: Dr. Robert H. Cox, Bockus Institute, Graduate Hospital, 19th and Lombard Streets, Philadelphia, Pa. 19146, U.S.A.
V o l u m e 74
T i i b i n g e n , a n d W. S c h a p e r ,
January/February
Bad Nauheim
Number 1
EDITORIAL Basic Res. Cardiol. 74, 1-9 (1979) 9 1979 Dr. Dietdch Steinkopff Verlag, Darmstadt ISSN 0300-8428
Bockus Institute, Graduate Hospital, and Department of Physiology, University of Pennsylvania, Philadelphia (USA)
C e n t r i b u t i e n ef s m e e t h m u s c l e te a r t e r i a l w a l l mechanics*) Beitrag der glatten Muskulatur zur M e c h a n i k der Arterienwand R . H. C o x With 4 figures (Received October 25, 1978)
Summary The contribution of vascular smooth muscle to the mechanical properties of arteries can be quantitated using elastomeric and classical muscle concepts. Such analyses can be performed using pressure-diameter data obtained from a given specimen u n d e r conditions of active and passive muscle. The elastomeric approach represents arterial wall mechanics in terms of incremental elastic moduli and theoretical characteristic impedance, z 0. Activation of muscle produces a reduction in values of incremental m o d u lu s at almost all values of transmural pressure. Values of Z 0 are increased at low pressure and decreased at high pressure following activation of muscle. In the muscle approach, the mechanics of arteries are quantitated in terms of active stress d e v e l o p m e n t and constriction responses as a function of muscle length and pressure, respectively. Active stress-muscle length and shortening-load relations obtained from arterial smooth muscle are qualitatively similar to those of other types of muscles. The length and load dependencies of these relations are what one would expect based on a sliding filament arrangement of contractile filaments. *) The research described herein from the author's laboratory was supported in part by Grant HL-17840 from U.S.P.H.S. 783
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Experimental methods have also been developed to study the properties of series elastic (SE) elements in these preparations. Load-extension relations of the SE are dependent on muscle length and anatomical site of the sample. With increasing muscle length, the SE appears to become stiffer. SE properties vary greatly in different preparations with a close correlation between SE stiffness and the maximum value of active force developed by the preparation. Neither of Hlll's three element models appear to be directly applicable in representing arterial SE, and its morphological basis is unclear. B l o o d vessels in the arterial circulation serve a n u m b e r of different functions. L a r g e arteries act as elastic reservoirs storing a p o r t i o n of the b l o o d ejected d u r i n g each heart beat (1). Small arteries in the circulation r e p r e s e n t the region w h e r e arterial p r e s s u r e a n d b l o o d flow d i s t r i b u t i o n are controlled b y n e u r o h u m o r a l m e c h a n i s m s (2). In addition, the wall of a n u m b e r of large to m e d i u m size arteries c o n t a i n specialized n e r v e e n d i n g s w h i c h act as " b a r o r e c e p t o r s " g e n e r a t i n g afferent nerve activity w h i c h is utilized b y the central n e r v o u s s y s t e m in the control of the circulation (3). The arterial s y s t e m m e e t s c h a n g e s in the short t e r m d e m a n d s of the o r g a n i s m t h r o u g h variations in the degree of activation of its v a s c u l a r s m o o t h muscle. I n q u a n t i t a t i n g the c o n t r i b u t i o n of v a s c u l a r s m o o t h m u s cle activity to the f u n c t i o n a l properties of arteries, two separate a p p r o a c h e s have b e e n developed. The first a p p r o a c h a t t e m p t s to define the effects of s m o o t h m u s c l e activation in t e r m s of its effect o n elastic properties a n d h e m o d y n a m i c p a r a m e t e r s of the circulation; this is the elastomeric a p p r o a c h (4-12). The s e c o n d a p p r o a c h a t t e m p t s to define the effects of activation in t e r m s of isometric force d e v e l o p m e n t a n d isotonic or isobaric shortening; this is the classical m u s c l e a p p r o a c h (8-14). The elastomeric a p p r o a c h is p r o b a b l y m o r e a p p r o p r i a t e l y applied to large arteries in the circulation, while the m u s c l e a p p r o a c h is p r o b a b l y m o r e applicable to the small arteries (the resistance vessels) in the circulation. While these two a p p r o a c h e s define the same p h y s i c a l / c h e m i c a l processes in the arterial s m o o t h muscle, a one-to-one c o r r e s p o n d e n c e b e t w e e n these r e p r e s e n t a t i o n s m a y n o t necessarily be expected. As b o t h of these a p p r o a c h e s are i m p o r t a n t to our u n d e r s t a n d i n g of the physiological function of the arterial wall, m e t h o d s h a v e b e e n d e v e l o p e d over the past few y e a r s to define the effects of activation of v a s c u l a r s m o o t h m u s c l e on arterial wall properties in t e r m s of b o t h a p p r o a c h e s u s i n g intact, isolated vascular s e g m e n t s (4-14). This brief d i s c u s s i o n will a t t e m p t to s u m m a r i z e s o m e of these results a n d indicates future areas of study. A detailed d e s c r i p t i o n of the m e t h o d s e m p l o y e d in the studies to be d e s c r i b e d is b e y o n d the s c o p e of this report. R e a d e r s are directed to the original studies (4-16). E x p e r i m e n t a l data are usually o b t a i n e d as p r e s s u r e - d i a m e t e r relations u n d e r c o n d i t i o n s of active a n d passive s m o o t h muscle. The f o r m e r is usually a c h i e v e d with m a x i m a l activation b y epinephrine, n o r e p i n e p h r i n e , p o t a s s i u m or the like. Passive c o n d i t i o n s are obtained u s i n g a variety of c h e m i c a l or m e c h a n i c a l means. P r e s s u r e / d i a m e t e r relations r e c o r d e d u n d e r c o n d i t i o n s of active a n d passive s m o o t h m u s c l e are used to q u a n t i t a t e the c o n t r i b u t i o n of s m o o t h m u s c l e to arterial wall p r o p e r t i e s u s i n g the two a p p r o a c h e s . I n t h e case of the classical m u s c l e a p p r o a c h these p r e s s u r e / d i a m e t e r data are u s e d to
Cox, ContributJon of smooth muscle
3
d e t e r m i n e v a l u e s of a c t i v e w a l l s t r e s s a n d a c t i v e d i a m e t e r r e s p o n s e as d e f i n e d in f i g u r e 1. T h e a c t i v e d i a m e t e r r e s p o n s e is o b t a i n e d as t h e d i f f e r e n c e in a r t e r i a l d i a m e t e r u n d e r a c t i v e a n d p a s s i v e c o n d i t i o n s at a g i v e n v a l u e of t r a n s m u r a l p r e s s u r e . T h e s e d i a m e t e r d i f f e r e n c e s m a y b e n o r m a l i z e d b y d i v i d i n g b y t h e p a s s i v e d i a m e t e r at e a c h p r e s s u r e level. A c t i v e s t r e s s r e s p o n s e s are q u a n t i t a t e d f r o m t h e d i f f e r e n c e in v a l u e s of w a l l s t r e s s u n d e r a c t i v e a n d p a s s i v e c o n d i t i o n s at a g i v e n v a l u e of b l o o d v e s s e l d i a m e t e r . V a l u e s of w a l l s t r e s s (ae) a r e d e t e r m i n e d f r o m p r e s s u r e ( P ) - d i a m e t e r d a t a u s i n g t h e f o l l o w i n g e q u a t i o n (17): a oe = ~
P
(I)
w h e r e a a n d b r e p r e s e n t t h e v a l u e of i n t e r n a l a n d e x t e r n a l radii, r e s p e c tively, at e a c h p r e s s u r e level. I n t h e e l a s t o m e r i c a p p r o a c h , t h e effects of s m o o t h m u s c l e a c t i v a t i o n are q u a n t i t a t e d in t e r m s of t w o v a r i a b l e s : t h e i n c r e m e n t a l e l a s t i c m o d u l u s and the characteristic impedance. The incremental elastic m o d u l u s repres e n t s t h e s l o p e of t h e t a n g e n t i a l s t r e s s - s t r a i n curve, a n d is c o m p u t e d u s i n g an e q u a t i o n of t h e s o r t (17): 2a2b AP E = -b2 a-------_ ~ Ab (2) V a l u e s of t h e o r e t i c a l c h a r a c t e r i s t i c i m p e d a n c e r e p r e s e n t t h e h i g h freq u e n c y a s y m p t o t e a b o u t w h i c h v a l u e s of v a s c u l a r i m p e d a n c e o s c i l l a t e (24), a n d r e p r e s e n t s t h e ratio of p u l s a t i l e p r e s s u r e a n d flow. It is d e t e r m i n e d p r i m a r i l y b y t h e e l a s t i c a n d g e o m e t r i c p r o p e r t i e s of t h e b l o o d
300
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TRANSMURAL PRESSURE
Fig. 1. Schematic summary of methods used in the representation of the active mechanics of arterial smooth muscle. A: Pressure-diameter relations obtained under conditions of active (left curve) and passive (right curve) smooth muscle. Isometric stress response and isobaric diameter response are defined in the diagram. Examples of values of isometric stress response at different values of norrealized diameter (panel B) and isobaric diameter response at different values of transmural pressure (panel C) are also shown.
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Basic Research in Cardiology, Vol. 74, No. 1 (1979)
v e s s e l s e g m e n t c l o s e to t h e m e a s u r e m e n t site, a n d d e t e r m i n e d f r o m t h e f o l l o w i n g e q u a t i o n (17): 1 ~/s (b 2 - a 2) ~ f ~ - ~ ~_-~ (3) Z0 ~a-----w h e r e s is t h e d e n s i t y of b l o o d . I n t h e left p a n e l of f i g u r e 2, t h e effects of s m o o t h m u s c l e a c t i v a t i o n on i n c r e m e n t a l e l a s t i c m o d u l u s of c a n i n e iliac a r t e r i e s a r e s h o w n . A c t i v a t i o n p r o d u c e s a r e d u c t i o n in v a l u e s of i n c r e m e n t a l e l a s t i c m o d u l u s at s p e c i f i c v a l u e s of t r a n s m u r a l p r e s s u r e (8). T h e m a g n i t u d e of t h i s r e d u c t i o n v a r i e s q u i t e c o n s i d e r a b l y at d i f f e r e n t t r a n s m u r a l p r e s s u r e s a n d in d i f f e r e n t s p e c i m e n s (8-12), a n d c a n be c o n s i d e r e d to b e a m e a s u r e of s m o o t h m u s c l e contractility. T h e v a r i a t i o n s of c h a r a c t e r i s t i c i m p e d a n c e w i t h t r a n s m u r a l p r e s s u r e is g i v e n in t h e r i g h t p a n e l of f i g u r e 2. U n d e r p a s s i v e c o n d i t i o n s , c h a r a c t e r i s tic i m p e d a n c e u s u a l l y i n c r e a s e s in a m o n o t o n i c f a s h i o n w i t h t r a n s m u r a l p r e s s u r e . U n d e r a c t i v a t e d c o n d i t i o n s , t h e r e is a m i n i m u m v a l u e of c h a r a c t e r i s t i c i m p e d a n c e at a p p r o x i m a t e l y 120 m m Hg. A t p r e s s u r e s a b o v e a n d below this value, characteristic i m p e d a n c e increases. S o m e vessels from s o m e s p e c i e s s h o w a d i f f e r e n t k i n d of b e h a v i o r u n d e r c o n d i t i o n s of p a s s i v e s m o o t h m u s c l e (8, 11). T h i s " U - s h a p e d " v a r i a t i o n of c h a r a c t e r i s t i c i m p e d a n c e w i t h t r a n s m u r a l p r e s s u r e is a g e n e r a l c h a r a c t e r i s t i c of all a r t e r i e s w i t h a c t i v a t e d m u s c l e . I t is i n t e r e s t i n g t h a t all v e s s e l s s t u d i e d a p p e a r to p o s s e s s a m i n i m u m v a l u e of c h a r a c t e r i s t i c i m p e d a n c e at a t r a n s m u r a l p r e s s u r e w i t h i n t h e a n i m a l ' s n o r m a l p h y s i o l o g i c a l r a n g e . It w o u l d be of i n t e r e s t to a s c e r t a i n if a c a u s a l r e l a t i o n e x i s t s b e t w e e n t h i s m i n i m u m a n d t h e n o r m a l v a l u e of a r t e r i a l p r e s s u r e i n a n a n i m a l . T h e d a t a s h o w n in f i g u r e 3 a r e r e p r e s e n t a t i v e of t h e a c t i v e m e c h a n i c a l p r o p e r t i e s of a r t e r i a l s m o o t h m u s c l e (4, 5, 8-13). T h e a c t i v e s t r e s s r e s p o n s e i n c r e a s e s n e a r l y l i n e a r l y in m a g n i t u d e to a m a x i m u m at s o m e o p t i m u m l e n g t h ( L ~ ) . F u r t h e r i n c r e a s e s in l e n g t h r e s u l t in a d e c r e a s e in t h e a c t i v e stress response. Such a relation b e t w e e n active force d e v e l o p m e n t and
o
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Fig. 2. Effects of smooth muscle activation on the variation of incremental elastic modulus and characteristic impedance with transmura] pressure. Data were obtained from a series of 12 canine renal arteries under conditions of active (closed squares) and passive (open circles) smooth muscle. Symbols are means while vertical bars are _+ 1 SEM.
Cox, Contribution of smooth muscle
5
m u s c l e l e n g t h is similar to that of o t h e r t y p e s of muscle, a n d s u g g e s t s a sliding filament t y p e a r r a n g e m e n t of the contractile a p p a r a t u s (18, 19). T h e active d i a m e t e r r e s p o n s e exhibits a similar variation with t r a n s m u r a l pressure. That is, a m a x i m u m value for this q u a n t i t y exists at p r e s s u r e s in the range of 50-150 m m H g . Substantial differences exist in t h e s e two m e a s u r e s of arterial s m o o t h m u s c l e f u n c t i o n related to age (6, 8, 9, 20), a n d a n a t o m i c a l location (10, 12) a m o n g other factors. The results given in these t w o figures s u m m a r i z e s the m a n n e r in w h i c h the c o n t r i b u t i o n of s m o o t h m u s c l e to arterial wall m e c h a n i c s can be q u a n t i t a t e d b y the two a p p r o a c h e s . This analysis also lends itself to the d e t e r m i n a t i o n of quantitative c h a n g e s or differences in the c o n t r i b u t i o n of s m o o t h m u s c l e to the m e c h a n i c a l properties of arteries. This, in fact, h a d b e e n d o n e in a n u m b e r of instances (8-12). I n general, the results indicate that the two different a p p r o a c h e s as well as the individual variables do n o t always yield the same conclusion. F o r example, a detailed c o m p a r i s o n of these responses have b e e n m a d e u s i n g carotid arteries from rat, rabbit, a n d dog (11). T h e m a x i m u m active stress r e s p o n s e was the s a m e in carotids f r o m rabbit a n d d o g a n d b o t h were larger t h a n that of the rat carotid. However, the m a x i m u m d i a m e t e r r e s p o n s e was largest in r a b b i t carotids while that of d o g and rat carotids were the same. Thus, the m a x i m u m d i a m e t e r r e s p o n s e for the rabbit carotids was larger t h a n that of the dog carotids in spite of the fact that t h e y p r o d u c e d the s a m e m a x i m u m stress response. T h e m a x i m u m d i a m e t e r r e s p o n s e was the same in d o g a n d rat carotids in spite of the fact that the rat carotids h a d a smaller m a x i m u m active stress r e s p o n s e c o m p a r e d to the d o g carotids. T h e decrease in i n c r e m e n t a l m o d u l u s with activation was the same in dog a n d rat carotids while b o t h were smaller t h a n that of the rabbit carotids. These differences were similar to the relative differences in d i a m e t e r responses. On the o t h e r hand, the effects of activation on the variations of Z0 w e r e largest in the rabbit carotids, and smallest in the d o g carotids with the rat carotids b e i n g intermediate. 3
0,75
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Fig. 3. Effects of smooth muscle activation analyzed by the muscle approach. The left panel shows the variation of isometric stress response as a function of normalized diameter. The right panel shows the variation of isobaric diameter response with transmural pressure. Symbols represent means, while horizontal and vertical bars are • 1 SEM for data averaged from 12 canine renal arteries.
6
Basic Research in Cardiology, Vol. 74, No. 1 (1979)
In other studies, arteries which exhibit larger stress responses produce l a r g e r (11, 21, 22) or t h e s a m e (8, 10, 11, 21) d i a m e t e r r e s p o n s e c o m p a r e d to a n o t h e r a r t e r y . Also, a r t e r i e s p r o d u c i n g t h e s a m e a c t i v e s t r e s s r e s p o n s e g e n e r a t e t h e s a m e (22) or a l a r g e r (11) d i a m e t e r r e s p o n s e . Thus, a c l e a r r e l a t i o n d o e s n o t a l w a y s e x i s t b e t w e e n t h e s e t w o m e a s u r e s of m u s c l e in d i f f e r e n t arteries. L i k e w i s e , t h e c o n t r i b u t i o n of s m o o t h m u s c l e in t h e e l a s t o m e r i c a p p r o a c h c a n p r o d u c e t h e s a m e c o n c l u s i o n s as d e t e r m i n e d w h e n a c t i v e d i a m e t e r r e s p o n s e s are e m p l o y e d (11, 21, 22) or w h e n a c t i v e s t r e s s r e s p o n s e s a r e e m p l o y e d (8, 10). I n o t h e r cases, d i f f e r e n t c o n c l u s i o n s c a n be r e a c h e d . O b v i o u s l y , no c l e a r r e l a t i o n e x i s t s b e t w e e n t h e s e v a r i o u s m e a s u r e s of t h e c o n t r i b u t i o n of s m o o t h m u s c l e a c t i v a t i o n to a r t e r i a l m e c h a n i c s e i t h e r b e t w e e n or w i t h i n t h e t w o a p p r o a c h e s . N u m e r o u s a d d i t i o n a l f a c t o r s c a n be i d e n t i f i e d t h a t c o u l d b e r e s p o n s i b l e for t h i s l a c k of u n a n i m i t y , s u c h as t h e p r e s e n c e of p a s s i v e t i s s u e e l e m e n t s c o u p l e d to t h e c o n t r a c t i l e a p p a r a t u s , t h e o r g a n i z a t i o n of t h e c o n t r a c t i l e a p p a r a t u s , i n t e r c e l l u l a r c o u p l i n g , o r g a n i z a t i o n of c o n t r a c t i l e u n i t s , t i s s u e c o m p r e s s i o n , w a l l t h i c k n e s s , etc. Clearly, t h e c o n t r i b u t i o n of s m o o t h m u s c l e to a r t e r i a l w a l l p r o p e r t i e s m u s t b e a s s e s s e d in t e r m s of s p e c i f i c v a r i a b l e s w i t h t h e k n o w l e d g e t h a t a g i v e n c o n c l u s i o n m a y n o t a p p l y if o t h e r v a r i a b l e s a r e c o n s i d e r e d . F u r t h e r m o r e , it is also c l e a r t h a t a d d i t i o n a l s t u d i e s m u s t b e u n d e r t a k e n to d e f i n e t h e f a c t o r s w h i c h d e t e r m i n e t h e s e i n t e r r e l a t i o n s in more quantitative terms. S i m i l a r to s t r i a t e d m u s c l e , a r t e r i a l s m o o t h m u s c l e b e h a v e s m e c h a n i c a l l y as if a p a s s i v e e l a s t i c s t r u c t u r e w e r e f u n c t i o n a l l y c o n n e c t e d in s e r i e s w i t h t h e c o n t r a c t i l e a p p a r a t u s (series elasticity). T h e p r e s e n c e of a subs t a n t i a l a m o u n t of s e r i e s e l a s t i c i t y in a r t e r i a l s m o o t h m u s c l e p r e p a r a t i o n s s u g g e s t s t h a t t h e s e p a s s i v e e l a s t i c s t r u c t u r e s h a v e c a p a c i t y to m o d i f y t h e e x p r e s s i o n of t h e i n t r i n s i c c h a r a c t e r i s t i c s of t h e m u s c l e c o n t r a c t i l e ele-
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Fig. 4. A summary of some mechanical properties of series elastic elements in arterial smooth muscle. The left panel shows the variation of canine iliac artery SE properties as a function of initial muscle length, and the right panel shows data from a number of arterial sites at a muscle length equivalent to Lmax-Symbols are identified in the inserts and represent means while bars represent _+ 1 SEM.
Cox, Contribution of smooth muscle
7
m e n t s m a n i f e s t as arterial wall r e s p o n s e s (12). It is p o s s i b l e to d e t e r m i n e t h e p r o p e r t i e s of t h e s e series elastic e l e m e n t s (SE) e x p e r i m e n t a l l y b y several different m e t h o d s . One of t h e characteristics of arterial s m o o t h m u s c l e is a v a r i a t i o n of series elasticity w i t h m u s c l e length (23). T h e left p a n e l of figure 4 s h o w s s u c h a v a r i a t i o n in iliac artery s m o o t h m u s c l e at six different v a l u e s of initial m u s c l e length. If the "Voigt m o d e l " of Hill c o u l d b e u s e d to r e p r e s e n t arterial s m o o t h m u s c l e all of t h e s e c u r v e s for different m u s c l e lengths w o u l d fall a l o n g a single u n i q u e curve. Since t h e y do not, it is c o n c l u d e d t h a t a Voigt t y p e of m o d e l is not a p p l i c a b l e to this p r e p a r a t i o n . If a " M a x w e l l m o d e l " w e r e applicable, t h e s e c u r v e s w o u l d all b e s u p e r i m p o s a b l e if t r a n s l a t e d to the origin of this graph, t h a t is, t h e y w o u l d h a v e t h e s a m e slopes. Since t h e y do not, it a p p e a r s t h a t a M a x w e l l t y p e of m o d e l is not a p p l i c a b l e either. This m e a n s t h a t a different f o r m of m o d e l m u s t b e d e v e l o p e d to r e p r e s e n t arterial s m o o t h m u s c l e . T h e d e v e l o p m e n t of s u c h a m o d e l is n e c e s s a r y for d e t e r m i n i n g t h e t r u e p r o p e r t i e s of t h e contractile a p p a r a t u s of v a s c u l a r s m o o t h m u s c l e a n d r e p r e s e n t s a n o t h e r f u t u r e a r e a for study. T h e p r o p e r t i e s of the SE in arterial s m o o t h m u s c l e also d e m o n s t r a t e a m a r k e d a n a t o m i c a l v a r i a t i o n (12). Results of e x p e r i m e n t s o n six different arterial sites are s u m m a r i z e d in the right p a n e l of figure 4. T h e s e m e a s u r e m e n t s of SE w e r e m a d e at a m u s c l e l e n g t h c o r r e s p o n d i n g to Lmax,i. e., t h e o p t i m u m length for active stress d e v e l o p m e n t in t h e s e p r e p a r a t i o n s . It is o b v i o u s t h a t a w i d e v a r i a t i o n in SE p r o p e r t i e s e x i s t at t h e s e different arterial sites, w i t h v a l u e s for t h e carotid a n d i n t e r n a l t h o r a c i c b e i n g t h e m o s t c o m p l i a n t a n d values f r o m t h e c o r o n a r y a n d m e s e n t e r i c arteries b e i n g the stiffest. I t is c o n c e i v a b l e t h a t a p o r t i o n of t h e s e d i f f e r e n c e s in SE m e c h a n i c a l p r o p e r t i e s is t h e result of d i f f e r e n c e s in t h e rest l e n g t h of SE in these preparations. E x p e r i m e n t a l e v i d e n c e exists to s u g g e s t t h a t t h e m a j o r p o r t i o n of SE in arterial s m o o t h m u s c l e resides outside of the contractile s y s t e m (15, 24). One p o t e n t i a l c a n d i d a t e for a m o r p h o l o g i c a l site for S E in arterial s m o o t h m u s c l e is the c o n n e c t i v e tissue m a t r i x t h a t c o u p l e s i n d i v i d u a l s m o o t h m u s c l e cells. Studies of b l o o d vessel m o r p h o l o g y indicate t h a t b o t h collag e n a n d elastin e x i s t in the m e d i a of large to small sized arteries (25-27). It is possible, therefore, t h a t t h e relative c o n t e n t of collagen a n d elastin m a y correlate w i t h t h e m e c h a n i c a l p r o p e r t i e s of the SE. H o w e v e r , e x p e r i m e n tal studies indicate t h a t no clear relation exists b e t w e e n c o n n e c t i v e tissue c o m p o s i t i o n of arteries a n d the m e c h a n i c a l p r o p e r t i e s of t h e i r SE. Obviously, t h e t r u e situation (i. e., the m o r p h o l o g i c a l basis for SE in arterial s m o o t h m u s c l e ) is m o r e c o m p l i c a t e d t h a n s i m p l y t h e relative a m o u n t of collagen a n d elastin in t h e b l o o d vessel. T h e identification of this basis for the SE is an i m p o r t a n t direction for s t u d y a n d m a y p r o v i d e i m p o r t a n t insight into t h e m e c h a n i s m of c o n t r a c t i o n a n d force t r a n s d u c t i o n . As i n d i c a t e d b y t h e m a g n i t u d e of the SE in t h e s e v a r i o u s arterial s m o o t h m u s c l e s , the p o t e n t i a l for a s u b s t a n t i a l distortion of the intrinsic p r o p e r ties of the contractile a p p a r a t u s is present.
8
Basic Research in Cardiology, Vol. 74, No. 1 (1979)
Zusammenfassung D e r Beitrag der glatten Muskulatur zu den meehanischen Eigenschaften der A_rterien kann auf der Grundlage zweier Muskelkonzepte quantifiziert werden, n~mlich der Elastizit~tslehre und des klassischen Konzepts. Derartige Analysen k6nnen unter V e r w e n d u n g der Daten von Druck und Durchmesser v o r g e n o m m e n werden, die m a n yon einem einzelnen Versuehsobjekt unter den Bedingungen der R u h e oder der Aktivit~t des Muskels erh~it. Das elastische Konzept beschreibt die Mechanik der Arterienwand in F o r m des tangentiellen elastischen Moduls und der charakteristischen Impedanz, Z o, Die Muskelaktivierung bewirkt eine A b n a h m e des tangentiellen Moduls bei fast allen transmuralen Druckwerten. Die Werte yon Z 0 steigen nach Aktivierung des Muskels bei niederen Drucken und n e h m e n bei hohen Drucken ab. B e i m klassischen Muskelkonzept wird die Mechanik der Arterien quantiflziert als aktive Spannungsentwicklung und Konstriktion als Funktion yon Muskell~nge oder Druck. Die aktiven L~ngen-Spannungs-Beziehungen und die Beziehung zwischen Verkfirzung und Last, die m a n von arteriellen glatten Muskeln erh~It, sind qualitativ ~hnlich wie bei anderen Muskeltypen. Die LAngenund Lastabh~/Igigkeit dieser Beziehungen sind so, wie m a n sie aufgrund des Gleitmodells der kontraktilen Filamente erwarten wfirde. Es wurden auch experimentelle Methoden entwickelt, u m die Eigenschaften des serienelastischen Elements an diesen Pr~paraten zu untersuchen. Die Beziehungen zwischen Last und Verl~ngerung des serienelastischen Elements h~ingen yon der Muskell~nge und der anatomischen Herkunft des PrAparates ab. Mit wachsender Niuskell~nge scheint das serienelastische Element steiferzu werden. Die serienelastischen Eigenschaften variierten stark bei verschiedenen Pr~parationen m i t einer e n g e n Korrelation zwischen der Steifheit des serienelastischen Elements u n d d e m m ax i m al en Wert der aktiven Kraftentwicklung des Pr~parates. Keines der DreiElementen-Modelle yon Hill scheint fiir die Beschreibung der Serienelastizit~it direkt an wen d b a r zu sein. Seine morphologische Grundlage ist unklar.
References 1. Mllnor, W. R.: Arterial im p e d a n c e as ventricular afterload. Circulation Res. 36, 565-570 (1975). 2. Ab b o u d , F. M.: Control of the various components of the peripheral vasculature. Fed. Proc. 31, 1226-1239 (1972). 3. Kirchheim, H. R.: Systemic arterial baroreceptor reflexes. Physiol. Rev. 56, 100-176 (1976). 4. Speden, 17. iV.: The m a i n t e n a n c e of arterial constriction at different transmural pressures. J. Physiol. 229, 361-381 (1973). 5. Dobrln, P. B., A. A. Rovick: Influence of vascular smooth muscle on contractile mechanics and elasticity of arteries. Am. J. Physiol. 217, 1644-1651 (1969). 6. Berry, C. L., S. E. Greenwald, J. F. Rivett: Static mechanical properties of the developing and mature rat aorta. Cardiovascular Res. 9, 669-678 (1975). 7. Busse, R., R. D. Bauer, Y. S u m m a , H. K 6 m e r , Th. Pasch: Comparison of the viseo-elastic properties of the tail artery in spontaneously hypertensive and n o r m o t e n s i v e rats. Pflfigers Arch. 364, 175-181 (1976). 8. Cox, R. H.: Effects of age on the mechanical properties of rat carotid artery. Am. J. Physiol. 233, H256-H263 (1977). 9. Cox, R. H., A. W. Jones, 1VI. L. Swain: Mechanics and electrolyte composition of arterial s m o o t h muscle in developing dogs. Am. J. Physiol. 231, 77-83 (1976). 10. Cox, R. H.: Arterial wall mechanics and composition and the effects of smooth muscle activation. Am. J. Physiol. 229, 807-812 (1975). 11. Cox, R. H.: Comparison of carotid artery mechanics in the rat, rabbit, and dog. Am. J. Physiol. 234, H280-H288 (1978).
Cox, Contribution of smooth muscle
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12. Cox, R. H.: Regional variation of series elasticity in canine arterial smooth muscles. Am. J. Physiol. 234, H542-H551 (1978). 13. Dobrin, P. B.: Isometric and isobaric contraction of carotid arterial smooth muscle. Am. J. Physiol. 225, 659-663 (1973). 14. Dobrin, P. B.: Vascular muscle series elastic element stiffness during isometric contraction. Circulation Res. 34, 242-250 (1974). 15. Cox, R. H.: Determination of series elasticity in arterial smooth muscle. Am. J. Physiol. 233, H248-H255 (1977). 16. Cox, R. H.: Three-dimensional mechanics of arterial segments in vitro: methods. J. Applied Physiol. 36, 381-384 (1974). 17. Cox, R. H.: Effects of norepinephrine on mechanics of arteries in vitro. Am. J. Physiol. 231, 420-425 (1976). 18. Johansson, B.: Mechanics of vascular smooth muscle contraction. Experientia 31, 1377-1476 (1975). 19. Murphy, R. A.: Contractile system function in m a m m a l i a n smooth muscle. Blood Vessels 13, 1-23 (1976). 20. Speden, R. IV.: Muscle load and constriction of the rabbit ear artery. J. Physiol. 248, 531-553 (1975). 21. Cox, R. H.: Arterial wall mechanics and composition in normal and spontaneously hypertensive rats. Fed. Proc. 37, 349 (1978). 22. Cox, R. 1,I.: Alterations in active and passive mechanics of rat carotid artery associated with experimental hypertension. Am. J. Physiol. (1978). Submitted for publication. 23. Cox, R. H.: Influence of muscle length on series elasticity in arterial smooth muscle. Am. J. Physiol. 234, C146-C154 (1978). 24. Dobrin, P., T. Canfield: Identification of smooth muscle series elastic compon e n t in intact carotid artery. Am. J. Physiol. 232, H122-H130 (1977). 25. Pease, D. C., S. Molinari: Electron microscopy of muscular arteries; Pial vessels of the cat and monkey. J. Ultrastructure Res. 3, 447-468 (1960). 26. Clis W. J.: The aortic tunica media in aging rats. Experimental and Molecular Pathology 13, 172-189 (1970). 27. Cox, R. H.: The mechanism of force transduction between vascular smooth muscle cells. In, Third Int. Symp. Vascular Neuroeffector Mechanisms, Eds. J. A. Bevan, et al. (Basel 1979). Author's address: Dr. Robert H. Cox, Bockus Institute, Graduate Hospital, 19th and Lombard Streets, Philadelphia, Pa. 19146, U.S.A.
