AMERICAN JOURNAL OF PHYSIOLOGY Vol. 229, No. 3, September 1975. Prinkd
Arterial
wall
in U.S.A.
mechanics
and composition
and the effects of smooth ROBERT H. COX Bockus Research Institute
and Department
muscle
of Physiology,
cox, ROBERT I-I. Arterial wall mechanics and composition and the eflects of smooth muscle activation. Am. J. Physiol. 229(3) : 8074312. 1975.-A comparison of passive mechanics and the effects of smooth muscle (SM) activation has been made in canine carotid and iliac arteries. Measurements of external diameter and axial force were made on isolated cylindrical segments in response to internal pressure variations. Data were obtained during maximal norepinephrine (NE) and potassium (K) activation, and following metabolic inhibition of SM. These data were used to determine wall tangential stress-strain relations. The maximum increase in wall stress after K and after NE was greater for the iliacs and occurred at smaller values of wall strain. Passive stress-strain curves for the iliacs were likewise shifted to smaller strains, suggesting an important role of passive wall elements in setting the length of contractile elements. Diameter responses to K at low values of pressure were the same for iliacs and carotids, but were better maintained at higher pressure levels for the iliacs. Similar findings were found for iliac responses to NE and K. The results suggest that at low values of wall stress, active diameter responses are not strongly dependent on the maximum isometric stress development. However, higher pressure-diameter responses are also determined by the force-generating capacity of SM. arterial sium;
smooth stress-strain
muscle; connective tissue; norepinephrine; relations; incremental elastic modulus
University
activation
of Pennsylvania,
Philade&hia,
Pennsylvania
19146
variations in passive stress-strain relations observed in blood vessels from various anatomical locations. The work described herein was performed in order to quantitate both the passive elastic characteristics of canine carotid and iliac arteries, and the effects of smooth muscle activation. These two arteries were chosen because of their different connective tissue compositions (11). The principal objective of this work was to correlate arterial wall mechanics and the effects of smooth muscle activation in arteries with different connective tissue content. METHODS
potas-
BEEN SUGGESTED that the external manifestation of the mechanical activity of muscle’s contractile elements is affected by the “passive” elastic properties of the tissue elements with which it is architecturally coupled (8, 17, 22). Such effects could be significant in arteries in which large amounts of connective tissue elements are found (11, 18, 27). As a result of the potential significance of this “interaction” of active and passive wall elements, it has also been suggested that changes in the passive elastic properties of a vessel may contribute to a change in its “reactivity” (17). A corollary to the latter is that differences in the passive elastic properties of arteries may contribute to differences in their reactivity. In fact, variations in passive elastic properties of blood vessels from various arterial sites do exist (1, 2) along with regional variations in arterial smooth muscle reactivity (3). It has been demonstrated that the connective tissue content of blood vessels also exhibits a regional variability (11). Since the mechanical properties of the principal connective tissue components (elastin (E) and collagen (C)) are considerably different, these variations in connective tissue have been suggested as the basis for the IT HAS
These experiments were performed on blood vessels from 20 healthy adult mongrel dogs either anesthetized with pentobarbital or acutely sacrificed with a captive bolt device. The blood vessels were rapidly dissected from the animals, freed of loose connective tissue and placed in a oxygenated (95 % 02, 5 % CO,), physiowarm (37”C), logical salt solution (PSS). The composition of this solution in millimoles per liter was as follows: 116.5 NaCl, 225 NaHC03, 1.2 NaHzPOq, 2.4 Na&Od, 4.5 KCl, 1.2 MgS04, 2.4 CaC12, and 5.6 dextrose. The pH of the solution was found to be 7.42 =t 0.03. The segment was mounted in the experimental apparatus at in vivo axial strain (stressed + unstressed axial length). The apparatus used in this study has been described in detail previously (4). One end of the segment was connected to the arm of an isometric force transducer for measurement of total axial force. The other end was connected to a manifold through which the inflation pressure was introduced. The external diameter of the blood vessel segment was measured near its midpoint using a semiconductor cantilever transducer. After incubating in the bath for at least 1 h, continuous inflation-deflation cycles were initiated. Pressure was continuously changed at a rate of 0.5 mmHg/s between 0 and 250 mmHg. After a variable number of these cycles (ca., 3-5)) reproducible curves of pressure-diameter and pressureaxial force were obtained and recorded on magnetic tape. These responses were used to derive passive stress-strain characteristics of the segments. Preliminary studies had demonstrated that after these initial procedures, incubation and conditioning, these particular blood vessels exhibited negligible smooth muscle (SM) “tone,” i.e., passive responses. This was verified for each vessel at the end of the experiment using metabolic inhibitors (cyanide, dinitrophenol, and iodoacetate) in PSS.
807
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808 Following initial recordings, pressure was set at 25 mmHg with a regulator. When the diameter had stabilized at a constant value, norepinephrine (NE) was added to the bath to a concentration of 5 pg/ml. After 2 min of constriction, pressure was lowered to 5 mmHg, and diameter followed until it stabilized (about 6-10 min after application of NE). The segment’s responses to inflation at 0.2 mmHg/s were obtained and recorded on tape. Af:er completion of the NE response, the bath was rinsed and refilled with PSS. Following reincubation for 1 h and additional conditioning by continuous inflation and deflation, the procedure used for NE was repeated. This time, however, the PSS was drained and replaced by a sirnilar solution in which all the sodium had been replaced by potassium(149 mM). The inflation response at 0.2 mmHg/s was recorded on tape. At the end of the experiment, the bloodvessel segment was removed from the bath, lightly blotted on filter paper, and weighed. The unstressed internal and external diameters were measured from a thin loop cut from the middle of the segment using a calibrated tool microscope. The data recorded on magnetic tape were played back after the experiment on an X-Y plotter. These data were used along with the segment weight and stressed and unstressed lengths to determine the three principal wall stress components, as described previously (4). The effects of SM activation were quantitated in two ways : first, the three-dimensional stress/external radius rehations were determined for passive, NE, and KC1 conditionsThe increase in wall stresses over passive values at a given value of radius associated with SM activation was obtained by interpolation and taken as a measure of active stress developed by SM for that radius. The second way in which the SM responses were quantitated was by determining the difference in mid-wall diameter between active and passive conditions at the same value of internal pressure. This dialerence was normalized by dividing by the passive va.lue. The quantity was taken as a measure of the ability of the SM to constrict the diameter of the blood vessel. In some instances more than one blood vessel was used from a specific animal. Those blood vessels that wGere not used immediately were placed in a metabolic incubator at 37°C and oxygenated with a gas mixture of 95 % 02 and 5 % COZ. When multiple blood vessels were studied from the same animal, the order in which they were used was randomly varied, i.e., right vs. left and carotid vs. iliac. The water and electrolyte content was determined from both fresh pieces and pieces of vessel that had been incubated for variable durations in PSS. Wet weight of tissues was determined after light blotting on filter paper. Dry tissue weights were determined after overnight drying at 95°C. The water content of the vessel segment was determined from the wet and dry weights. The electrolyte content was determined with an atomic-absorption spectrophotometer. The methods used for analysis of water and electrolyte content have been described in detail previously (18). The specific electrolytes determined included calcium, magnesium, potassium, sodium, and chloride. The connective tissue composition was determined using a modification of the method of Neuman and Logan (11, 21). The elastin and collagen fractions of the blood vessels were separated into soluble and insoluble components under
R.
heat and pressure, proline contents.
and
quantitated
from
their
H.
COX
hydroxy-
RESULTS
Examples of records obtained from carotid (top) and iliac (bottom) arteries are shown in Fig. 1. The pressure-diameter curves during inflation are shifted to lower diameters at all levels of internal pressure following NE and KC1 activation. In the case of the pressure/axial force curves, the axial force is increased during inflation by both NE and KC1 at all pressures excep t the lowest for the iliac. In all cases the curve for KC1 is shifted to smaller diameters relative to the NE response for both carotid and iliac arteries. Similarly, axial force is generally greater in response to KC1 relative to NE for both vessels at any given value of pressure. Figure 2 shows a summary of some passive mechanical properties averaged from all blood vessels studied. The graph to the left shows the relationship between passive tangential wall stress and normalized external wall radius. The wall radius was normalized by dividing the radius by the value at zero pressure and in vivo length (bo). Data points of stress and normalized ra .dius were averaged at specific values of internal pressure from 0 to 250 mmHg in steps of 10 mmHg. Values of average tangential stress
30
LI
FORCE 20
(gm) IO Lpep--I
0
I 0.3
I 0.2
DIAMETER FORCE
y-1 0.4
0.5
km)
(gm)
2501
0’
DIAMETER
km)
1. On-line records of internal pressure-external diameter to right) and internal pressure-axial force (curves to left) for a (A) and an iliac (B) artery. Continuous curves are passive relations, long-dashed curves are norepinephrine responses, and shortdashed curves are potassium responses. Arrows show direction of pressure change. FIG.
(curves carotid
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MECHANICS
AND
COMPOSITION.
OF
809
ARTERIRS 1.5
1.0
1.4
0
1.8
NORMQLlZED EXTERNAL RdOlUS WB)
125 INTERNIL
PRESSURE
250 ,mmHg,
FIG. 2. A: a comparison of passive tangential stress versus normalized external radius’ for. data averaged from all iliac (closed squares) and all carotid (open circles) arteries. Horizontal and vertical bars are SEMs. External radius was normalized by dividing by value at zero pressure and in vivo length. B: a comparison of ‘incremental elastic modulus vs. internal pressure for 2 artery groups (same. symbds as A).
(as) were computed from the relation (4, 10, 26):
ae = a
b -a
pi
0
1.0
NORMALIZED
___1__--I 1.4
EXTERNAL
1.8
RADIUS
FIG. 3. Comparison of normalized external radius dependence of tangential stress response for both iliac (squares) and carotid (circles) arteries in response to norepinephrine (open symbols) and potassium (closed symbols). External radius was normalized by dividing by value at zero pressure and in vivo length. Values of wall-stress responses were obtained at selected values of normalized radii from various experiments by interpolation and averaged.
(4
where Pi is the internal pressure,and a and b are the internal and external radii, respectively. Data averaged from 12 iliac and 12 carotid arteries are summarized. There is no significant difference between the stress-radiuscurves of the two artery groups at values of normalized radius below about 1.6. Above 1.6 the stress-radiuscurve for the iliac risesmore rapidly than that of the carotid, and the value of normalized radius is smaller for the iliac at any given level of wall stress. The graph on the right shows the relationship between incremental elastic modulus and interna pressure for the two groups of blood vessels.The incremental elastic modulus (E) was obtained from the experimental data using the following equation (2) : INTERNAL
where ~8is the tangential strain. Although the arterial wall is in fact anisotropic, the incrementa elastic modulus is a reasonable estimate of the. tengential ainisotropic elastic modulus (9). It is apparent that at any given level of internal pressure above about 60 mmHg the incremental elastic modulus is always larger for the iliac artery reetive ‘( to the carotid. Figure 3 summarizes the relationship between the increasein tangential stressand normalized external radius for the iliac and carotid arteries follotiing NE and K activation. The normalized diameter responsesfrom the same experiments are summarized in Fig. 4 at values of internal pressure. A number of features of thesetwo figures are apparent. For the conditions employed in this study, K produces a consistently larger response for both arteries. The peak tangential stressresponsefor the iliac arteries was approximately 42% greater with K compared. to NE. For the carotid, the ratio was approximately 38%. The peak
PRESSURE
hnmHg1
FIG. 4. Comparison
of internal pressure dependence of normalized mid-wall diameter reduction for iliac (squares) and carotid (circles) arteries in response to norepinephrine (open symbols) and potassium (closed symbols). Diameter response was normalized by dividing by passive value at each pressure. Latter were averaged at specific values of internal pressure from all experiments.
tangential stressresponseoccurred as a smaller normalized external radius for the iliacs. The maximum normalized diameter responsefor the iliac arteries was 12% larger for KC1 compared to NE. The maximum diameter response produced by KC1 was not statistically different for the two groups of blood vessels(-51.8 f 2.3 % for the iliacs and -49.2 f 4.2% for the carotids). Thus KCl, which produced the same maximum diameter reduction in these two groups of arteries, produced a smaller wall-stress responsein the case of the carotid. A summary of the analysis for connective tissue, water, and electrolyte content of the two groups of blood vesselsis
Downloaded from www.physiology.org/journal/ajplegacy by ${individualUser.givenNames} ${individualUser.surname} (129.237.035.237) on January 19, 2019.
810
R.
H.
COX
1. Summary of connective tissue, water, and electrolyte content of carotid and iliac arteries _______I_____-~~
TABLE
Site
Condition
Hz0
Ca
K
m
g/kg wet wt
Carotid (n =
Fresh
711
Incubated
Fresh (n =
12) Incubated
Values chloride;
*l
k7.5
12)
Iliac
are means C, collagen;
mmol/kg
755* *3
12.3 .o
10.0
13.3* rto.5
721 zt4.6
15.2 zt1.3
10.6 ztO.8
715 It2
25.9* zt4.9
11.6* zko.7
are
as follows : HzO, water * Statistically significant
dry wt
125 zk3.3
ho.4
25.2* xt4.0
rf: SE. Symbols and E, elastin.
Na
124 *3 119 zt3.9 87* &12
content; Ca, compared
given in Table 1. There is little difference in the total water content and the total connective tissue content (C + E) for these two groups of blood vessels. However, the relative amounts of collagen and elastin are considerably different. The iliac contains less collagen but more elastin than the carotid, producing a significantly lower C/E ratio. The potassium and magnesium contents of these blood vessels are essentially the same. These two ions are primarily located intracellularly, which suggests that the total cell solid content of these blood vessels is similar. A comparison has been made of the connective tissue, water, and electrolyte contents in fresh tissue samples and samples incubated in PSS for 2 h; this is also given in Table 1. There is generally an increase in water content and all electrolytes except potassium. No significant changes in connective tissue content were observed as a result of incubation. DISCUSSION
The results described in this study demonstrate that differences exist in arterial wall mechanics and responses after smooth muscle activation in blood vessels with different connective tissue content. Passive mechanics data (Fig. 2) show that the iliac artery has a higher incremental elastic modulus than the carotid at equivalent values of internal pressure. Also, the passive stress-strain curve is shifted to the left for the iliac arteries primarily at higher values of stress (ca., above 1 X 1 O6 dyn/cm2). These results are somewhat unexpected in view of past studies and traditional concepts (5, 23). Previous studies from this laboratory on changes in carotid artery mechanics in puppies demonstrated that values of elastic modulus at 100 mmHg increased with increasing C/E ratio during growth and development (5). Also, stress-strain curves were shown to be shifted to the left with the increasing C/E ratio during aging. The results of the current study appear not to be in agreement with the concepts developed in the classical study of Roach and Burton (23). From their concepts, it would have been anticipated that the stress-strain curve for the carotids would be shifted to the left of that of the iliacs and that the elastic modulus of the former would be larger than the latter. Since two different arterial sites are being compared in this study, this discussion suggests that other
314 AZ15
270 Ax19
51.8 zkl.3
25.2 ztO.8
It12
354* *ll
54.7 ztl.4
27.0 zt1.7
343 All
293 +7
44.5 xkl .o
32.9 Ifio.9
374 zt20
319* zk7
42.9 k1.6
34.4 *2.3
397%
calcium ; Rig, magnesium with fresh data, P >
; K,
potassium;
Na,
sodium;
Cl,
.05.
factors, such as the distribution and coupling of connective tissue elements, may also be important in determining passive mechanics. The maximum stress response for the iliacs occurred at a lower value of normalized radius (strain) than for the carotids (Fig. 3). This latter difference is approximately the same as the difference in passive stress-strain relations for the two arteries (Fig. 2). This suggests that the passive tissue elements in the arterial wall play an important role in wall reactivity by determining the length of the contractile elements. It would follow that changes in the elastic properties of the passive wall elements could indeed alter reactivity at a given internal pressure, for example, as previously suggested (17). Dobrin and Canfield (8) have described another way in which passive elements arranged functionally in series with the contractile elements can modify smooth muscle responses. These series-coupled elements can also distort the relation between wall strain and contractile element strain in a manner that depends on their elastic properties. Although the responses following SM activation determined in this study are considered as measures of active (isometric and isobaric) responses of the SM, their equivalence is by no means proven. Dobrin (7) has determined carotid artery SM responses as isometric responses during activation with NE and as inflation responses of arteries with previously activated SM. He found these responses to be the same when isometric responses were performed at strains below the peak of the active length-tension curve. Speden and Freckelton (25), on the other hand, have shown that pressure-diameter curves were shifted upward when analyzed as inflation responses with previously contracted SM compared with deflation responses after activation. Since the latter’s activations were performed at high pressures (and strains), this result is as expected from Dobrin’s study (7) and is not inconsistent with his conclusions. The relation between the inflation responses as recorded herein and “active length-force” relations as determined by more classical methods depends, among other factors, on the force-velocity-length relations of the SM. As the contracted SM is actively lengthened, the latter is “operating” on the negative side of the force-velocity curve, i.e., at forces above PO and negative velocities of shortening. The
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MECHANICS
AND
COMPOSITION
OF
811
ARTERIES
force (or stress in this case) determined at any particular muscle length will depend on both the isometric lengthforce curve and the force-velocity curve and on the rate of lengthening (i.e., the strain rate). The smaller the strain rate, the better will be the approximation of the recorded force to the actual isometric value. As the strain rate approaches zero, inflation force approaches isometric force. The strain rates produced by constant inflation vary over the course of the inflation because of the nonlinear pressurediameter curves of activated arteries (Fig. 1). Strain rates are lowest for the steepest slopes (i.e., at low and high pressures) and largest at the smallest slopes (middle pressure range). In these experiments, average strain rates were of the order of 0.0007 s-l (range 0.0002-0.0030 s-l). This is to be compared with reported normalized V,., for arterial SM between 0.07 and 1.8 s-l (14, 16, 20). Using data given by Herlihy and Murphy (16) on force-velocity relations of hog carotid artery medial strips, a strain rate of +0.0007 s-l would overestimate PO by 4 % assuming that the forcevelocity curve could be directly extrapolated for forces above PO. Although the latter assumption may not be true in striated muscle (19), no information is available, to my knowledge, concerning its validity in vascular smooth muscle. Therefore, the best estimates of isometric force would be obtained during periods of low strain rate, while during higher strain rates isometric force may be overestimated by some, as yet undetermined, amount. It was also found in this study that differences existed in the diameter responses after smooth muscle activation by high K (Fig. 4). No difference was found in the maximum normalized diameter response for the two arteries or in the responses at low internal pressure levels (ca., O-50 mmHg). At higher pressure levels, however, the diameter responses for the iliacs were better maintained. It is reasonable to expect that diameter reductions for a sliding filament arrangement of contractile proteins (24) at low levels of wall stress (or strain) would be more closely related to the structural relations between filaments than the absolute amount of contractile protein present. That is, the important determinant of diameter reduction at low wall stress is the total shortening capability of the contractile filaments. On
the other hand, at higher values of passive wall stress the diameter response would be expected to also be determined by the amount of contractile protein and its total forcegenerating capacity. Thus, the iliacs with a greater stress response are better able to maintain diameter responses with increasing values of internal pressure (i.e., passive wall stress). A comparison of NE and K responses for the iliacs also The maximum stress response supports this explanation. was 42 % higher for K, but the maximum diameter reduction was only increased by 12 Yo. Also, over the low internal the diameter reductions pressure range (ca., O-40 mmHg), were essentially equal. At higher pressure levels, diameter reductions were better rnaintained during K contractures. The responses of the carotids to NE and K were considerably different compared to the iliacs. A simple explanation for these differences is not readily apparent at this time. The results described herein show both qualitative and quantitative similarities to results obtained by others using different experimental methods. In terms of diameter responses to activation, the magnitude and the pressure range for optimal response are sirnilar to those reported by several investigators (6, 12, 25). For example, the rnaximum normalized diameter response for the carotids was - 20 70, which compares closely to the value of - 23 Yo obtained by Dobrin (6). S’imilarly, the wall-stress responses following activation also showed many sirnilarities to previously published data. These responses (Fig. 3) were highly strain dependent, demonstrated a maximal response, and were Such characteristics of vascular decidedly asymmetric. smooth muscle length-tension (or stress-strain) curves have been previously described by numerous investigators using a variety of methods and preparations (e.g., 6, 10, 13, 15). The author is grateful to Dr. I,. H. Peterson for his support, encouragement, and suggestions during the course of this research. The helpful discussions and suggestions of Drs. Allan W. Jones, Emil Monos, and Grace M. Fischer are also gratefully acknowledged, as is the valuable technical assistance of Miss Elaine Veit. This work was supported in part by Program Project Research Grant HL-07762 from the Public Health Service. Received
for
publication
3 1 October
1974.
REFERENCES 1. ATTINGER, E., A. ANNE, AND H. SUGAWARA. Modeling of pressure flow relations in arteries and veins. In: Hemorheology, edited by A. L. Copley. Oxford: Pergamon, 1968, p. 2555276. 2. BERGEL, D. H. The static elastic properties of the arterial wall. J. Physiol., London 156 : 445-457, 1961. 3. BOHR, D. F. Individualities among vascular smooth muscles. In: Electrolytes and Cardiovascular Diseases, edited by E. Bajusz. Base1 : Karger, 1965, p. 342355. 4. COX, R. H. Three-dimensional mechanics of arterial segments in vitro : methods. J. A/@. Physiol. 36 : 38 l--384, 1974. 5. Cox, K. H., A. W. JONES, AND G. M. FISCHER. Carotid artery mechanics, connective tissue, and electrolyte changes in puppies. Am. J. i’hysiol. 227: 563-568, 1974. 6. DOBRIN, P. B. Isometric and isobaric contraction of carotid arterial smooth muscle. Am. J. Physiol. 225: 659-663, 1973. 7. DOBRIN, P. B. Influence of initial length on length-tension relationship of vascular smooth muscle. Am. J. Physiol. 225 : 664-670, 1973. 8. DOBRIN, P. B., AND T. R. CANFIELD. Series elastic and contractile elements in vascular smooth muscle. Circulation Res. 33: 454-464, 1974. 9. DOBRIN, P. B., AND J. M. DOYLE. Vascular smooth muscle and the anisotropy of dog carotid artery. CircuZation Res. 27 : 105- 119, 1970.
10. DOBRIN, P. B., AND A. A. ROVICK. Influence of vascular smooth muscle on contractile mechanics and elasticity of arteries. Am. J. Physiol. 217: 1644-1651, 1969. 11. FISCHER, G. h/l., AND J. G. LI,AURADO. Collagen and elastin content in canine arteries selected from functionally different vascular beds. Circulatzon Res. 19 : 394-399, 1966. 12* GORE, R. E. Wall stress: a determinant of regional differences in response of frog microvessels to norepinephrine. Am. J. Physiol. 222: 82-91, 1971. 13. HANSEN, T. EL, G. D. ABRAMS, AND D. F. BOIJR. Role of pressure in structural and functional changes in arteries of hypertensive rats. Circulation Res. 34, Suppl. 1 : I 10 1-T 107, 1974. 14. HELLSTRAND, P., AND B. JOHANSSON. The force-velocity relations in venous smooth muscle. Acta Physiol. Stand. 91 : 45&46A, 1974. 15. HERLIHY, J. T., AND R. A. IV~RPHY. Length-tension relationship of smooth muscle of the hog carotid artery. Circulation Res. 33: 275283, 1973. 16. 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. 17. JOHANSSON, B. Determinants of vascular reactivity. Federation Proc. 33: 121-126, 1974.
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812 18. JONES, A. W., AND M. L. SWAIN. Chemical and kinetic analysis of sodium distribution in canine lingual artery. Am. J. Physiul. 223: 1110-1118, 1972. 19. KATZ, B. The relation between force and speed in muscular contraction. J. Physiol., London 96: 45-64, 1939. 20. LASZT, L. On the physiology of vascular smooth muscle in different regions. In : Proc. Symp. Physiol. Pharmacol. Vas. Neuroeffector Systems, edited by J. A. Bevan et al. Basel: S. Karger, 1971, p. 263-272. 21. NEUMAN, R. E., AND M. A. LOGAN. The determination of hydroxyproline. J. Biol. Chem. 184 : 299-306, 1950. 22. PROSSER, C. L. Smooth muscle. Ann. Rev. Physiol. 36: 503-535, 1974. 23. ROACH, M. R., AND A. C. BURTON. The reason for the shape of the
R. distensibility
curves
of arteries.
Can.
J. Biochem.
Physiol.
H.
COX
35 : 68 I-
690, 1957. 24:. SOMLYO, A.
Filament 25.
P., C. E. DEVINE, A. V. SOMLYO, AND R. V. RICE. organization in vertebrate smooth muscle. Phil. Trans.
Roy. Sot. London, SPEDEN, R. N.,
Ser. 3 265: 223-229, 1973. AND D. J. FRECKEL,TON. Constriction pressures. Circulation Res. 26 and
high transmural II 99-H 112, 1970. 26. VAISHNAV, R. N., J. T. YOUNG, J. S. JANICKI, Nonlinear anisotropic elastic properties of the ;phys. J. 12: 1008-1027, 1972. 27. WJEDERHIELM, C. A. Distensibility characteristics vessels. Federation Proc. 24 : 1075- 1084, 1965.
of arteries 27, Suppl.
ac II :
AND D. J. PATEL.
canine
aorta.
of small
Bioblood
Downloaded from www.physiology.org/journal/ajplegacy by ${individualUser.givenNames} ${individualUser.surname} (129.237.035.237) on January 19, 2019.
Arterial
wall
in U.S.A.
mechanics
and composition
and the effects of smooth ROBERT H. COX Bockus Research Institute
and Department
muscle
of Physiology,
cox, ROBERT I-I. Arterial wall mechanics and composition and the eflects of smooth muscle activation. Am. J. Physiol. 229(3) : 8074312. 1975.-A comparison of passive mechanics and the effects of smooth muscle (SM) activation has been made in canine carotid and iliac arteries. Measurements of external diameter and axial force were made on isolated cylindrical segments in response to internal pressure variations. Data were obtained during maximal norepinephrine (NE) and potassium (K) activation, and following metabolic inhibition of SM. These data were used to determine wall tangential stress-strain relations. The maximum increase in wall stress after K and after NE was greater for the iliacs and occurred at smaller values of wall strain. Passive stress-strain curves for the iliacs were likewise shifted to smaller strains, suggesting an important role of passive wall elements in setting the length of contractile elements. Diameter responses to K at low values of pressure were the same for iliacs and carotids, but were better maintained at higher pressure levels for the iliacs. Similar findings were found for iliac responses to NE and K. The results suggest that at low values of wall stress, active diameter responses are not strongly dependent on the maximum isometric stress development. However, higher pressure-diameter responses are also determined by the force-generating capacity of SM. arterial sium;
smooth stress-strain
muscle; connective tissue; norepinephrine; relations; incremental elastic modulus
University
activation
of Pennsylvania,
Philade&hia,
Pennsylvania
19146
variations in passive stress-strain relations observed in blood vessels from various anatomical locations. The work described herein was performed in order to quantitate both the passive elastic characteristics of canine carotid and iliac arteries, and the effects of smooth muscle activation. These two arteries were chosen because of their different connective tissue compositions (11). The principal objective of this work was to correlate arterial wall mechanics and the effects of smooth muscle activation in arteries with different connective tissue content. METHODS
potas-
BEEN SUGGESTED that the external manifestation of the mechanical activity of muscle’s contractile elements is affected by the “passive” elastic properties of the tissue elements with which it is architecturally coupled (8, 17, 22). Such effects could be significant in arteries in which large amounts of connective tissue elements are found (11, 18, 27). As a result of the potential significance of this “interaction” of active and passive wall elements, it has also been suggested that changes in the passive elastic properties of a vessel may contribute to a change in its “reactivity” (17). A corollary to the latter is that differences in the passive elastic properties of arteries may contribute to differences in their reactivity. In fact, variations in passive elastic properties of blood vessels from various arterial sites do exist (1, 2) along with regional variations in arterial smooth muscle reactivity (3). It has been demonstrated that the connective tissue content of blood vessels also exhibits a regional variability (11). Since the mechanical properties of the principal connective tissue components (elastin (E) and collagen (C)) are considerably different, these variations in connective tissue have been suggested as the basis for the IT HAS
These experiments were performed on blood vessels from 20 healthy adult mongrel dogs either anesthetized with pentobarbital or acutely sacrificed with a captive bolt device. The blood vessels were rapidly dissected from the animals, freed of loose connective tissue and placed in a oxygenated (95 % 02, 5 % CO,), physiowarm (37”C), logical salt solution (PSS). The composition of this solution in millimoles per liter was as follows: 116.5 NaCl, 225 NaHC03, 1.2 NaHzPOq, 2.4 Na&Od, 4.5 KCl, 1.2 MgS04, 2.4 CaC12, and 5.6 dextrose. The pH of the solution was found to be 7.42 =t 0.03. The segment was mounted in the experimental apparatus at in vivo axial strain (stressed + unstressed axial length). The apparatus used in this study has been described in detail previously (4). One end of the segment was connected to the arm of an isometric force transducer for measurement of total axial force. The other end was connected to a manifold through which the inflation pressure was introduced. The external diameter of the blood vessel segment was measured near its midpoint using a semiconductor cantilever transducer. After incubating in the bath for at least 1 h, continuous inflation-deflation cycles were initiated. Pressure was continuously changed at a rate of 0.5 mmHg/s between 0 and 250 mmHg. After a variable number of these cycles (ca., 3-5)) reproducible curves of pressure-diameter and pressureaxial force were obtained and recorded on magnetic tape. These responses were used to derive passive stress-strain characteristics of the segments. Preliminary studies had demonstrated that after these initial procedures, incubation and conditioning, these particular blood vessels exhibited negligible smooth muscle (SM) “tone,” i.e., passive responses. This was verified for each vessel at the end of the experiment using metabolic inhibitors (cyanide, dinitrophenol, and iodoacetate) in PSS.
807
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808 Following initial recordings, pressure was set at 25 mmHg with a regulator. When the diameter had stabilized at a constant value, norepinephrine (NE) was added to the bath to a concentration of 5 pg/ml. After 2 min of constriction, pressure was lowered to 5 mmHg, and diameter followed until it stabilized (about 6-10 min after application of NE). The segment’s responses to inflation at 0.2 mmHg/s were obtained and recorded on tape. Af:er completion of the NE response, the bath was rinsed and refilled with PSS. Following reincubation for 1 h and additional conditioning by continuous inflation and deflation, the procedure used for NE was repeated. This time, however, the PSS was drained and replaced by a sirnilar solution in which all the sodium had been replaced by potassium(149 mM). The inflation response at 0.2 mmHg/s was recorded on tape. At the end of the experiment, the bloodvessel segment was removed from the bath, lightly blotted on filter paper, and weighed. The unstressed internal and external diameters were measured from a thin loop cut from the middle of the segment using a calibrated tool microscope. The data recorded on magnetic tape were played back after the experiment on an X-Y plotter. These data were used along with the segment weight and stressed and unstressed lengths to determine the three principal wall stress components, as described previously (4). The effects of SM activation were quantitated in two ways : first, the three-dimensional stress/external radius rehations were determined for passive, NE, and KC1 conditionsThe increase in wall stresses over passive values at a given value of radius associated with SM activation was obtained by interpolation and taken as a measure of active stress developed by SM for that radius. The second way in which the SM responses were quantitated was by determining the difference in mid-wall diameter between active and passive conditions at the same value of internal pressure. This dialerence was normalized by dividing by the passive va.lue. The quantity was taken as a measure of the ability of the SM to constrict the diameter of the blood vessel. In some instances more than one blood vessel was used from a specific animal. Those blood vessels that wGere not used immediately were placed in a metabolic incubator at 37°C and oxygenated with a gas mixture of 95 % 02 and 5 % COZ. When multiple blood vessels were studied from the same animal, the order in which they were used was randomly varied, i.e., right vs. left and carotid vs. iliac. The water and electrolyte content was determined from both fresh pieces and pieces of vessel that had been incubated for variable durations in PSS. Wet weight of tissues was determined after light blotting on filter paper. Dry tissue weights were determined after overnight drying at 95°C. The water content of the vessel segment was determined from the wet and dry weights. The electrolyte content was determined with an atomic-absorption spectrophotometer. The methods used for analysis of water and electrolyte content have been described in detail previously (18). The specific electrolytes determined included calcium, magnesium, potassium, sodium, and chloride. The connective tissue composition was determined using a modification of the method of Neuman and Logan (11, 21). The elastin and collagen fractions of the blood vessels were separated into soluble and insoluble components under
R.
heat and pressure, proline contents.
and
quantitated
from
their
H.
COX
hydroxy-
RESULTS
Examples of records obtained from carotid (top) and iliac (bottom) arteries are shown in Fig. 1. The pressure-diameter curves during inflation are shifted to lower diameters at all levels of internal pressure following NE and KC1 activation. In the case of the pressure/axial force curves, the axial force is increased during inflation by both NE and KC1 at all pressures excep t the lowest for the iliac. In all cases the curve for KC1 is shifted to smaller diameters relative to the NE response for both carotid and iliac arteries. Similarly, axial force is generally greater in response to KC1 relative to NE for both vessels at any given value of pressure. Figure 2 shows a summary of some passive mechanical properties averaged from all blood vessels studied. The graph to the left shows the relationship between passive tangential wall stress and normalized external wall radius. The wall radius was normalized by dividing the radius by the value at zero pressure and in vivo length (bo). Data points of stress and normalized ra .dius were averaged at specific values of internal pressure from 0 to 250 mmHg in steps of 10 mmHg. Values of average tangential stress
30
LI
FORCE 20
(gm) IO Lpep--I
0
I 0.3
I 0.2
DIAMETER FORCE
y-1 0.4
0.5
km)
(gm)
2501
0’
DIAMETER
km)
1. On-line records of internal pressure-external diameter to right) and internal pressure-axial force (curves to left) for a (A) and an iliac (B) artery. Continuous curves are passive relations, long-dashed curves are norepinephrine responses, and shortdashed curves are potassium responses. Arrows show direction of pressure change. FIG.
(curves carotid
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MECHANICS
AND
COMPOSITION.
OF
809
ARTERIRS 1.5
1.0
1.4
0
1.8
NORMQLlZED EXTERNAL RdOlUS WB)
125 INTERNIL
PRESSURE
250 ,mmHg,
FIG. 2. A: a comparison of passive tangential stress versus normalized external radius’ for. data averaged from all iliac (closed squares) and all carotid (open circles) arteries. Horizontal and vertical bars are SEMs. External radius was normalized by dividing by value at zero pressure and in vivo length. B: a comparison of ‘incremental elastic modulus vs. internal pressure for 2 artery groups (same. symbds as A).
(as) were computed from the relation (4, 10, 26):
ae = a
b -a
pi
0
1.0
NORMALIZED
___1__--I 1.4
EXTERNAL
1.8
RADIUS
FIG. 3. Comparison of normalized external radius dependence of tangential stress response for both iliac (squares) and carotid (circles) arteries in response to norepinephrine (open symbols) and potassium (closed symbols). External radius was normalized by dividing by value at zero pressure and in vivo length. Values of wall-stress responses were obtained at selected values of normalized radii from various experiments by interpolation and averaged.
(4
where Pi is the internal pressure,and a and b are the internal and external radii, respectively. Data averaged from 12 iliac and 12 carotid arteries are summarized. There is no significant difference between the stress-radiuscurves of the two artery groups at values of normalized radius below about 1.6. Above 1.6 the stress-radiuscurve for the iliac risesmore rapidly than that of the carotid, and the value of normalized radius is smaller for the iliac at any given level of wall stress. The graph on the right shows the relationship between incremental elastic modulus and interna pressure for the two groups of blood vessels.The incremental elastic modulus (E) was obtained from the experimental data using the following equation (2) : INTERNAL
where ~8is the tangential strain. Although the arterial wall is in fact anisotropic, the incrementa elastic modulus is a reasonable estimate of the. tengential ainisotropic elastic modulus (9). It is apparent that at any given level of internal pressure above about 60 mmHg the incremental elastic modulus is always larger for the iliac artery reetive ‘( to the carotid. Figure 3 summarizes the relationship between the increasein tangential stressand normalized external radius for the iliac and carotid arteries follotiing NE and K activation. The normalized diameter responsesfrom the same experiments are summarized in Fig. 4 at values of internal pressure. A number of features of thesetwo figures are apparent. For the conditions employed in this study, K produces a consistently larger response for both arteries. The peak tangential stressresponsefor the iliac arteries was approximately 42% greater with K compared. to NE. For the carotid, the ratio was approximately 38%. The peak
PRESSURE
hnmHg1
FIG. 4. Comparison
of internal pressure dependence of normalized mid-wall diameter reduction for iliac (squares) and carotid (circles) arteries in response to norepinephrine (open symbols) and potassium (closed symbols). Diameter response was normalized by dividing by passive value at each pressure. Latter were averaged at specific values of internal pressure from all experiments.
tangential stressresponseoccurred as a smaller normalized external radius for the iliacs. The maximum normalized diameter responsefor the iliac arteries was 12% larger for KC1 compared to NE. The maximum diameter response produced by KC1 was not statistically different for the two groups of blood vessels(-51.8 f 2.3 % for the iliacs and -49.2 f 4.2% for the carotids). Thus KCl, which produced the same maximum diameter reduction in these two groups of arteries, produced a smaller wall-stress responsein the case of the carotid. A summary of the analysis for connective tissue, water, and electrolyte content of the two groups of blood vesselsis
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810
R.
H.
COX
1. Summary of connective tissue, water, and electrolyte content of carotid and iliac arteries _______I_____-~~
TABLE
Site
Condition
Hz0
Ca
K
m
g/kg wet wt
Carotid (n =
Fresh
711
Incubated
Fresh (n =
12) Incubated
Values chloride;
*l
k7.5
12)
Iliac
are means C, collagen;
mmol/kg
755* *3
12.3 .o
10.0
13.3* rto.5
721 zt4.6
15.2 zt1.3
10.6 ztO.8
715 It2
25.9* zt4.9
11.6* zko.7
are
as follows : HzO, water * Statistically significant
dry wt
125 zk3.3
ho.4
25.2* xt4.0
rf: SE. Symbols and E, elastin.
Na
124 *3 119 zt3.9 87* &12
content; Ca, compared
given in Table 1. There is little difference in the total water content and the total connective tissue content (C + E) for these two groups of blood vessels. However, the relative amounts of collagen and elastin are considerably different. The iliac contains less collagen but more elastin than the carotid, producing a significantly lower C/E ratio. The potassium and magnesium contents of these blood vessels are essentially the same. These two ions are primarily located intracellularly, which suggests that the total cell solid content of these blood vessels is similar. A comparison has been made of the connective tissue, water, and electrolyte contents in fresh tissue samples and samples incubated in PSS for 2 h; this is also given in Table 1. There is generally an increase in water content and all electrolytes except potassium. No significant changes in connective tissue content were observed as a result of incubation. DISCUSSION
The results described in this study demonstrate that differences exist in arterial wall mechanics and responses after smooth muscle activation in blood vessels with different connective tissue content. Passive mechanics data (Fig. 2) show that the iliac artery has a higher incremental elastic modulus than the carotid at equivalent values of internal pressure. Also, the passive stress-strain curve is shifted to the left for the iliac arteries primarily at higher values of stress (ca., above 1 X 1 O6 dyn/cm2). These results are somewhat unexpected in view of past studies and traditional concepts (5, 23). Previous studies from this laboratory on changes in carotid artery mechanics in puppies demonstrated that values of elastic modulus at 100 mmHg increased with increasing C/E ratio during growth and development (5). Also, stress-strain curves were shown to be shifted to the left with the increasing C/E ratio during aging. The results of the current study appear not to be in agreement with the concepts developed in the classical study of Roach and Burton (23). From their concepts, it would have been anticipated that the stress-strain curve for the carotids would be shifted to the left of that of the iliacs and that the elastic modulus of the former would be larger than the latter. Since two different arterial sites are being compared in this study, this discussion suggests that other
314 AZ15
270 Ax19
51.8 zkl.3
25.2 ztO.8
It12
354* *ll
54.7 ztl.4
27.0 zt1.7
343 All
293 +7
44.5 xkl .o
32.9 Ifio.9
374 zt20
319* zk7
42.9 k1.6
34.4 *2.3
397%
calcium ; Rig, magnesium with fresh data, P >
; K,
potassium;
Na,
sodium;
Cl,
.05.
factors, such as the distribution and coupling of connective tissue elements, may also be important in determining passive mechanics. The maximum stress response for the iliacs occurred at a lower value of normalized radius (strain) than for the carotids (Fig. 3). This latter difference is approximately the same as the difference in passive stress-strain relations for the two arteries (Fig. 2). This suggests that the passive tissue elements in the arterial wall play an important role in wall reactivity by determining the length of the contractile elements. It would follow that changes in the elastic properties of the passive wall elements could indeed alter reactivity at a given internal pressure, for example, as previously suggested (17). Dobrin and Canfield (8) have described another way in which passive elements arranged functionally in series with the contractile elements can modify smooth muscle responses. These series-coupled elements can also distort the relation between wall strain and contractile element strain in a manner that depends on their elastic properties. Although the responses following SM activation determined in this study are considered as measures of active (isometric and isobaric) responses of the SM, their equivalence is by no means proven. Dobrin (7) has determined carotid artery SM responses as isometric responses during activation with NE and as inflation responses of arteries with previously activated SM. He found these responses to be the same when isometric responses were performed at strains below the peak of the active length-tension curve. Speden and Freckelton (25), on the other hand, have shown that pressure-diameter curves were shifted upward when analyzed as inflation responses with previously contracted SM compared with deflation responses after activation. Since the latter’s activations were performed at high pressures (and strains), this result is as expected from Dobrin’s study (7) and is not inconsistent with his conclusions. The relation between the inflation responses as recorded herein and “active length-force” relations as determined by more classical methods depends, among other factors, on the force-velocity-length relations of the SM. As the contracted SM is actively lengthened, the latter is “operating” on the negative side of the force-velocity curve, i.e., at forces above PO and negative velocities of shortening. The
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MECHANICS
AND
COMPOSITION
OF
811
ARTERIES
force (or stress in this case) determined at any particular muscle length will depend on both the isometric lengthforce curve and the force-velocity curve and on the rate of lengthening (i.e., the strain rate). The smaller the strain rate, the better will be the approximation of the recorded force to the actual isometric value. As the strain rate approaches zero, inflation force approaches isometric force. The strain rates produced by constant inflation vary over the course of the inflation because of the nonlinear pressurediameter curves of activated arteries (Fig. 1). Strain rates are lowest for the steepest slopes (i.e., at low and high pressures) and largest at the smallest slopes (middle pressure range). In these experiments, average strain rates were of the order of 0.0007 s-l (range 0.0002-0.0030 s-l). This is to be compared with reported normalized V,., for arterial SM between 0.07 and 1.8 s-l (14, 16, 20). Using data given by Herlihy and Murphy (16) on force-velocity relations of hog carotid artery medial strips, a strain rate of +0.0007 s-l would overestimate PO by 4 % assuming that the forcevelocity curve could be directly extrapolated for forces above PO. Although the latter assumption may not be true in striated muscle (19), no information is available, to my knowledge, concerning its validity in vascular smooth muscle. Therefore, the best estimates of isometric force would be obtained during periods of low strain rate, while during higher strain rates isometric force may be overestimated by some, as yet undetermined, amount. It was also found in this study that differences existed in the diameter responses after smooth muscle activation by high K (Fig. 4). No difference was found in the maximum normalized diameter response for the two arteries or in the responses at low internal pressure levels (ca., O-50 mmHg). At higher pressure levels, however, the diameter responses for the iliacs were better maintained. It is reasonable to expect that diameter reductions for a sliding filament arrangement of contractile proteins (24) at low levels of wall stress (or strain) would be more closely related to the structural relations between filaments than the absolute amount of contractile protein present. That is, the important determinant of diameter reduction at low wall stress is the total shortening capability of the contractile filaments. On
the other hand, at higher values of passive wall stress the diameter response would be expected to also be determined by the amount of contractile protein and its total forcegenerating capacity. Thus, the iliacs with a greater stress response are better able to maintain diameter responses with increasing values of internal pressure (i.e., passive wall stress). A comparison of NE and K responses for the iliacs also The maximum stress response supports this explanation. was 42 % higher for K, but the maximum diameter reduction was only increased by 12 Yo. Also, over the low internal the diameter reductions pressure range (ca., O-40 mmHg), were essentially equal. At higher pressure levels, diameter reductions were better rnaintained during K contractures. The responses of the carotids to NE and K were considerably different compared to the iliacs. A simple explanation for these differences is not readily apparent at this time. The results described herein show both qualitative and quantitative similarities to results obtained by others using different experimental methods. In terms of diameter responses to activation, the magnitude and the pressure range for optimal response are sirnilar to those reported by several investigators (6, 12, 25). For example, the rnaximum normalized diameter response for the carotids was - 20 70, which compares closely to the value of - 23 Yo obtained by Dobrin (6). S’imilarly, the wall-stress responses following activation also showed many sirnilarities to previously published data. These responses (Fig. 3) were highly strain dependent, demonstrated a maximal response, and were Such characteristics of vascular decidedly asymmetric. smooth muscle length-tension (or stress-strain) curves have been previously described by numerous investigators using a variety of methods and preparations (e.g., 6, 10, 13, 15). The author is grateful to Dr. I,. H. Peterson for his support, encouragement, and suggestions during the course of this research. The helpful discussions and suggestions of Drs. Allan W. Jones, Emil Monos, and Grace M. Fischer are also gratefully acknowledged, as is the valuable technical assistance of Miss Elaine Veit. This work was supported in part by Program Project Research Grant HL-07762 from the Public Health Service. Received
for
publication
3 1 October
1974.
REFERENCES 1. ATTINGER, E., A. ANNE, AND H. SUGAWARA. Modeling of pressure flow relations in arteries and veins. In: Hemorheology, edited by A. L. Copley. Oxford: Pergamon, 1968, p. 2555276. 2. BERGEL, D. H. The static elastic properties of the arterial wall. J. Physiol., London 156 : 445-457, 1961. 3. BOHR, D. F. Individualities among vascular smooth muscles. In: Electrolytes and Cardiovascular Diseases, edited by E. Bajusz. Base1 : Karger, 1965, p. 342355. 4. COX, R. H. Three-dimensional mechanics of arterial segments in vitro : methods. J. A/@. Physiol. 36 : 38 l--384, 1974. 5. Cox, K. H., A. W. JONES, AND G. M. FISCHER. Carotid artery mechanics, connective tissue, and electrolyte changes in puppies. Am. J. i’hysiol. 227: 563-568, 1974. 6. DOBRIN, P. B. Isometric and isobaric contraction of carotid arterial smooth muscle. Am. J. Physiol. 225: 659-663, 1973. 7. DOBRIN, P. B. Influence of initial length on length-tension relationship of vascular smooth muscle. Am. J. Physiol. 225 : 664-670, 1973. 8. DOBRIN, P. B., AND T. R. CANFIELD. Series elastic and contractile elements in vascular smooth muscle. Circulation Res. 33: 454-464, 1974. 9. DOBRIN, P. B., AND J. M. DOYLE. Vascular smooth muscle and the anisotropy of dog carotid artery. CircuZation Res. 27 : 105- 119, 1970.
10. DOBRIN, P. B., AND A. A. ROVICK. Influence of vascular smooth muscle on contractile mechanics and elasticity of arteries. Am. J. Physiol. 217: 1644-1651, 1969. 11. FISCHER, G. h/l., AND J. G. LI,AURADO. Collagen and elastin content in canine arteries selected from functionally different vascular beds. Circulatzon Res. 19 : 394-399, 1966. 12* GORE, R. E. Wall stress: a determinant of regional differences in response of frog microvessels to norepinephrine. Am. J. Physiol. 222: 82-91, 1971. 13. HANSEN, T. EL, G. D. ABRAMS, AND D. F. BOIJR. Role of pressure in structural and functional changes in arteries of hypertensive rats. Circulation Res. 34, Suppl. 1 : I 10 1-T 107, 1974. 14. HELLSTRAND, P., AND B. JOHANSSON. The force-velocity relations in venous smooth muscle. Acta Physiol. Stand. 91 : 45&46A, 1974. 15. HERLIHY, J. T., AND R. A. IV~RPHY. Length-tension relationship of smooth muscle of the hog carotid artery. Circulation Res. 33: 275283, 1973. 16. 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. 17. JOHANSSON, B. Determinants of vascular reactivity. Federation Proc. 33: 121-126, 1974.
Downloaded from www.physiology.org/journal/ajplegacy by ${individualUser.givenNames} ${individualUser.surname} (129.237.035.237) on January 19, 2019.
812 18. JONES, A. W., AND M. L. SWAIN. Chemical and kinetic analysis of sodium distribution in canine lingual artery. Am. J. Physiul. 223: 1110-1118, 1972. 19. KATZ, B. The relation between force and speed in muscular contraction. J. Physiol., London 96: 45-64, 1939. 20. LASZT, L. On the physiology of vascular smooth muscle in different regions. In : Proc. Symp. Physiol. Pharmacol. Vas. Neuroeffector Systems, edited by J. A. Bevan et al. Basel: S. Karger, 1971, p. 263-272. 21. NEUMAN, R. E., AND M. A. LOGAN. The determination of hydroxyproline. J. Biol. Chem. 184 : 299-306, 1950. 22. PROSSER, C. L. Smooth muscle. Ann. Rev. Physiol. 36: 503-535, 1974. 23. ROACH, M. R., AND A. C. BURTON. The reason for the shape of the
R. distensibility
curves
of arteries.
Can.
J. Biochem.
Physiol.
H.
COX
35 : 68 I-
690, 1957. 24:. SOMLYO, A.
Filament 25.
P., C. E. DEVINE, A. V. SOMLYO, AND R. V. RICE. organization in vertebrate smooth muscle. Phil. Trans.
Roy. Sot. London, SPEDEN, R. N.,
Ser. 3 265: 223-229, 1973. AND D. J. FRECKEL,TON. Constriction pressures. Circulation Res. 26 and
high transmural II 99-H 112, 1970. 26. VAISHNAV, R. N., J. T. YOUNG, J. S. JANICKI, Nonlinear anisotropic elastic properties of the ;phys. J. 12: 1008-1027, 1972. 27. WJEDERHIELM, C. A. Distensibility characteristics vessels. Federation Proc. 24 : 1075- 1084, 1965.
of arteries 27, Suppl.
ac II :
AND D. J. PATEL.
canine
aorta.
of small
Bioblood
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