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The mechanical properties of the aorta of the cephalopod mollusc, Octopus dofleini (Wulker) Shadwick, Robert Edward 1982

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THE MECHANICAL PROPERTIES OF THE AORTA OF THE CEPHALOPOD MOLLUSC, OCTOPUS DOFLEINI (WULKER) by ROBERT EDWARD SHADWICK B.Sc, The Unversity of Western Ontario, 1975 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Zoology We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1982 Robert Edward Shadwick, 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date Ike /_5 jl± DE-6 (.3/81) 1 i i ABSTRACT In any c i r c u l a t o r y system, the mechanical properties of the walls of the a r t e r i e s w i l l have s i g n i f i c a n t e f f e cts on the dynamics of blood flow. The d i s t e n s i b i 1 i t y of the artery wall is important in determining the wave propagation c h a r a c t e r i s t i c s of the system, as well as contributing a pulse smoothing effect on the intermittant flow of blood from the heart. These properties are well studied in mammalian ci r c u l a t o r y systems, but have never been d i r e c t l y investigated in any invertebrate animal. This study examines the structure and mechanical properties of the major artery in a cephalopod mollusc, Octopus d o f l e i n i , and relates these properties to cardiovascular dynamics in the l i v i n g animal. The dorsal aorta of cephalopods i s the large blood vessel through which blood flows from the systemic heart. The walls of this artery are comprised of thick layers of c i r c u l a r l y and lon g i t u d i n a l l y oriented muscle c e l l s . Outside the muscle layers is a loose collagenous adventitia. Innermost, adjacent to the lumen i s a layer of e l a s t i c f i b r e s , analogous to vertebrate e l a s t i n f i b r e s . In addition, these fibres extend throughout the artery wall as a network of e x t r a c e l l u l a r connective tissue. . The e l a s t i c fibres have been isolated from the octopus aorta and subjected to di r e c t mechanical and chemical tests. These fibres are composed of a protein which has rubber-like properties, that i s , the material has high e x t e n s i b i l i t y and i i i a m o d u l u s o f e l a s t i c i t y , G (= 4.65 X 10 N/m ) , w h i c h i s s i m i l a r t o a r u b b e r . C h e m i c a l and o p t i c a l p r o p e r t i e s o f t h i s u n u s u a l p r o t e i n s u g g e s t t h a t t h e m o l e c u l a r s t r u c t u r e i s one o f c o v a l e n t l y c r o s s l i n k e d , random c o i l , k i n e t i c a l l y f r e e c h a i n s . T h i s i n t e r p r e t a t i o n i s c o n s i s t e n t w i t h t h e t h e r m o e l a s t i c d a t a f o r t h e s e p r o t e i n f i b r e s w h i c h f i t c l o s e l y t h e p r e d i c t i o n s o f t h e k i n e t i c t h e o r y o f e n t r o p i c e l a s t i c i t y i n r u b b e r s . I n v i t r o m e c h a n i c a l t e s t s on t h e o c t o p u s a o r t a showed t h a t t h i s v e s s e l i s a h i g h l y d i s t e n s i b l e , r e s i l i e n t e l a s t i c t u b e w h i c h , l i k e mammalian a r t e r i e s , becomes much l e s s c o m p l i a n t a s i t i s e x t e n d e d . The t a n g e n t i a l e l a s t i c m o d u l u s i n t h e c i r c u m f e r e n t i a l d i r e c t i o n ( E c ) r a n g e d f r o m 9 X 1 0 t o 2 X 1 0 N/m o v e r t h e n o r m a l r e s t i n g r a n g e o f p h y s i o l o g i c a l p r e s s u r e s (20 t o 50 cm o f w a t e r ) , w h i l e t h e e l a s t i c m o d u l u s i n t h e l o n g i t u d i n a l d i r e c t i o n ( E l ) was a l w a y s a b o u t o n e - h a l f o f E c . H y s t e r e s i s i n q u a s i - s t a t i c i n f l a t i o n s was a b o u t 25%. The d y n a m i c m o d u l u s o f e l a s t i c i t y i n c r e a s e d c o n t i n u o u s l y w i t h f r e q u e n c i e s f r o m 0.1 Hz t o 10Hz. Tan d v a r i e d f r o m a b o u t 0.10 t o 0.15 o v e r t h e p h y s i o l o g i c a l l y r e l e v a n t r a n g e of f r e q u e n c i e s i n t h i s a n i m a l (0.1 t b 1.0 H z ) . T h e s e r e s u l t s show t h a t t h i s a r t e r y c a n f u n c t i o n a s an e l a s t i c , p u l s e s m o o t h i n g component i n t h e o c t o p u s c i r c u l a t i o n . F u r t h e r , i t a p p e a r s t h a t t h e e l a s t i c p r o p e r t i e s o f t h e i n t a c t a r t e r y c a n be a t t r i b u t e d l a r g e l y t o . t h e r u b b e r - l i k e p r o t e i n f o u n d i n t h e w a l l . I n v i v o m e a s u r e m e n t s o f b l o o d p r e s s u r e a n d ' f l o w i n t h e iv octopus show an impedance spectrum which i s similar to what has been observed in t u r t l e s and frogs, that i s , the a r t e r i a l c i r c u l a t i o n of this invertebrate i s adequately described by a simple Windkessel model. Pulse wave v e l o c i t y measured in vivo appeared to be greater than 10 m/sec, although the velocity predicted from the e l a s t i c properties of the aorta was less than 5 m/sec. These anomalies arise because, due to the low heart rate of the octopus, the length of the aorta i s less than 5% of the wavelength of the s i g n i f i c a n t frequencies in the pressure pulse. The a r t e r i a l system of the octopus i s one which is dominated by strong wave r e f l e c t i o n s , but does not exhibit other transmission effects such as peaking and d i s t o r t i o n of the t r a v e l l i n g pressure wave. These results may have general application to other cephalopods, but i t w i l l be interesting to examine species, such as pelagic squids, which presumably have higher blood pressure and heart rates. V TABLE OF CONTENTS ABSTRACT 1 i TABLE OF CONTENTS v LIST OF TABLES ix LIST OF FIGURES x ACKNOWLEDGEMENTS x i i i I. INTRODUCTION 1 II. THE STRUCTURE OF THE OCTOPUS AORTA 8 A. Introduction 8 B. Methods 1 1 C. Results 13 1. Histology 1 3 2. Ultrastructure 20 D. Discussion 33 III. CHEMICAL AND MECHANICAL PROPERTIES OF OCTOPUS ELASTIC FIBRES 39 A. Introduction 39 B. Rubber E l a s t i c i t y 40 1. Network Properties 40 2. Thermoelasticity 47 C. Methods 52 1. Composition of the Artery Wall 52 a. Water content 52 b. E l a s t i c f i b r e content 52 c. Collagen content 53 2. Isolation of E l a s t i c Fibres 54 3. S o l u b i l i t y of the IE Fibres 54 4. Composition of the E l a s t i c Fibres 55 v i a. Water content 55 b. Protein content 55 c. Carbohydrate content 56 5. Amino Acid Analysis 56 6. Force-Extension Tests 57 7. Thermoelastic Tests 60 a. Length-temperature measurements 60 b. Force-temperature measurements 61 8. Optical Properties 62 D. Results 63 1. Composition of the Artery Wall 63 2. Properties of Isolated E l a s t i c Fibres 65 3. Amino Acid Analyses 66 4. Force-Extension Tests 69 5. Optical Properties 72 6. Thermoelasticity 77 E. Discussion 86 1. Network Properties 86 2. Thermoelastic Properties 89 3. The Role of the E l a s t i c Fibres in the Octopus Aorta 92 IV. MECHANICAL PROPERTIES OF THE OCTOPUS AORTA 95 A. Introduction 95 B. An a l y t i c a l Methods 98 1 . Linear E l a s t i c i t y 98 2. Nonlinear E l a s t i c i t y in Thick-walled Tubes 100 3. V i s c o e l a s t i c Behaviour 105 4. Dynamic Incremental E l a s t i c i t y 108 v i i C. Experimental Methods 110 1. In f l a t i o n Experiments 110 2. Uniaxial Force-Extension Tests 116 D. Results 121 1. Infl a t i o n Experiments 121 2. Activation of Vascular Muscle 125 3. Uniaxial Tests 131 4. Calculation of Ec from Inf l a t i o n Experiments 133 5. Vi s c o e l a s t i c Properties 140 E. Discussion 148 1. Mechanical Properties of the Aorta 148 2. Structural Basis of Non-Linear E l a s t i c i t y 151 3. The Octopus Aorta as an E l a s t i c Reservoir 154 V. HEMODYNAMICS OF THE OCTOPUS ARTERIAL CIRCULATION 156 A. Introduction 156 B. Methods 163 1. Measurement of Aortic Blood Pressure and Flow 163 2. Determination of the Input Impedance 166 3. Theoretical Determination of the Input Impedance 169 4. Determination of the Pressure Wave Velocity 169 C. Results 174 1. Aortic Blood Pressure and Flow in the Resting Octopus 174 2. Aortic Impedance Spectra 177 3. Application of the Windkessel Model 183 4. Pressure Wave Propagation in the Aorta 189 Pressure Wave Velocity Measurements in v i t r o 195 D. Discussion 199 1. Pressure and Flow Waveforms 199. 2. Reflection E f f e c t s on Wave Velocity and Impedance 201 3. The Input Impedance in the Octopus Windkessel 208 VI. SUMMARY 212 REFERENCES 216 ix LIST OF TABLES Table 3.1 Amino acid analyses 68 Table 3.2 Thermoelastic data at 20 degrees C. 84 Table 4.1 V i s c o e l a s t i c data 146 Table 5.1 Predicted pressure wave ve l o c i t y 190 X LIST OF FIGURES Figure 1.1 Cephalopod c i r c u l a t o r y anatomy 2 Figure 2.1 Diagram of a transverse section of the octopus aorta 14 Figure 2.2 Light micrographs of the octopus aorta 16 Figure 2.3 Scanning electron micrographs of the octopus aorta 19 Figure 2.4 Longitudinal section of the octopus aorta 22 Figure 2.5 Electron micrographs of the octopus aorta 24 Figure 2.6 Longitudinal sections of the aorta 26 Figure 2.7 Transverse sections of the longitudinal muscle 28 Figure 2.8 Collagen fibres in the aorta 32 Figure 3.1 The idealised random c o i l molecule 42 Figure 3.2 Thermoelastic curves for rubber 51 Figure 3.3 E l a s t i c fibres on the micro force transducer 59 Figure 3.4 E l a s t i c f i b r e content of the aorta 64 Figure 3.5 Force extension data for native fibres 70 Figure 3.6 Force extension data for p u r i f i e d f i b r e s 71 Figure 3.7 Combined force extension r a t i o data 73 Figure 3.8 Non-Gaussian properties of the IE f i b r e s 74 Figure 3.9 Birefringence of the e l a s t i c fibres 76 Figure 3.10 Length temperature data for e l a s t i c fibres 78 Figure 3.11 Force temperature plots 79 Figure 3.12 Force length isotherms from data of F i g . 3.11 83 Figure 3.13 Force length curve for fibres resolved into enthalpy, entropy and internal energy 85 Figure 3.14 Force extension curves for rubber-like proteins 90 Figure 4.1 Linear and non-linear stress s t r a i n curves 99 x i Figure 4.2 Diagram of an a r t e r i a l segment to show dimensions and to i l l u s t r a t e Poisson's ra t i o s 101 Figure 4.3 Diagram of the i n f l a t i o n apparatus 111 Figure 4.4 Diagram of uniaxial test specimens 118 Figure 4.5 Quasi-static pressure volume curves 122 Figure 4.6 Pressure versus circumferential and longitudinal strains 124 Figure 4.7 Stress str a i n curves from i n f l a t i o n data 126 Figure 4.8 Drug effects on pressure volume curves 128 Figure 4.9 Stress str a i n curves for data of F i g . 4.8 130 Figure 4.10 Uniaxial force extension curves 132 Figure 4.11 Uniaxial stress s t r a i n curves 134 Figure 4.12 Tangential e l a s t i c moduli from uniaxial data 135 Figure 4.13 Circumferential e l a s t i c modulus as a function of pressure 137 Figure 4.14 Circumferential e l a s t i c modulus as a function of s t r a i n 138 Figure 4.15 Stress relaxation and recovery in an aorta 141 Figure 4.-16 Dynamic mechanical testing of the aorta 143 Figure 4.17 Dynamic mechanical data 144 Figure 4.18 Comparison of non-linear e l a s t i c i t y in the octopus aorta and the OAE protein 153 Figure 5.1 The Windkessel model 158 Figure 5.2 The T piece cannula used in the aorta 164 Figure 5.3 The apparatus for in v i t r o pressure wave vel o c i t y measurement 171 Figure 5.4 Analogue pressure and flow in the aorta 175 Figure 5.5 D i g i t i s e d and signal averaged pressure and flow data 177 Figure 5.6 Amplitude of pressure and flow harmonics 179 Figure 5.7 Aortic impedance spectra 180 x i i Figure 5.8 Impedance data compared to the Windkessel predictions 184 Figure 5.9 Flow components through the Windkessel 187 Figure 5.10 A pressure pulse in the aorta recorded simultaneously at two locations 192 Figure 5.11 Apparent wave vel o c i t y and transmission measured in v i t r o 196 Figure 5.12 Apparent v e l o c i t y curves plotted against the r e l a t i v e wavelength 204 Figure 5.13 Calculated impedance modulus curve compared to Zo and the experimental data 209 x i i i ACKNOWLEDGEMENTS It i s with great pleasure that I thank my research supervisor, John Gosline, for his valuable advice, his generous support and his undying enthusiasm during the course of t h i s study. I am also grateful to my wife, K r i s t i n a , for an abundance of moral support over the past six years, and for a great deal of help with the production of t h i s thesis. I also wish to thank the members of my research commitee, Peter Hochachka, David Jones, John P h i l l i p s and David Randall for helpful discussions and for the use of much of their laboratory f a c i l i t i e s . Laszlo Veto and Wayne Vogl were excellent tutors in my endeavours to learn electron microscopy techniques. Meyer Aaron offered advice with experimental techniques used in Chapter III, and designed one of the computer programs used in Chapter V. B i l l Milsom provided the surgical expertise for the physiological studies in Chapter V. Arthur Martin kindly donated some of the octopuses used in thi s study, and provided much p r a c t i c a l advice on how to handle the beasts! 1 CHAPTER I. INTRODUCTION Among invertebrate animals, the cephalopod molluscs are generally considered to be one of the most "advanced" groups. To many zoologists t h i s d i s t i n c t i o n i s readily attributed to the fact that cephalopods have impressive jet locomotory c a p a b i l i t i e s , as well as a remarkably complex nervous system including a r e l a t i v e l y large brain, eyes which are s u p e r f i c i a l l y l i k e those of vertebrates, and extensive development of peripheral nervous networks throughout the body (Wells, 1978). It i s not so well appreciated by most that the system of blood c i r c u l a t i o n in cephalopods i s also highly developed, by invertebrate standards, such that in many ways i t is functionally analogous to c i r c u l a t o r y systems in vertebrates (Martin and Johansen, 1966; Packard, 1972). In cephalopods the c i r c u l a t o r y system i s e s s e n t i a l l y a "closed" one, that i s , a r t e r i e s and veins are linked by c a p i l l a r y networks in a l l tissues (Williams, 1902; Barber and Graziadei, 1965; Kawaguti, 1970; Browning, 1979, 1982). Venous hemocoels, which are predominant in other mol'luscan c i r c u l a t i o n s , have been greatly reduced in cephalopods so that blood volume is only about 6% of the body weight (as compared to 40 to 80% in other molluscs; Martin and Johansen, 1966). Some d e t a i l s of the c i r c u l a t o r y anatomy of coleoid cephalopods ( i . e . octopus, squid and c u t t l e f i s h ) are shown in Figure 1.1. A single-chambered v e n t r i c l e pumps blood into the 2 Figure 1 . 1 . Diagram of the major components of the c i r c u l a t o r y anatomy of a coleoid cephalopod. Arrows indicate the d i r e c t i o n of blood flow. 3 systemic c i r c u l a t i o n for d i s t r i b u t i o n to the various body regions. The major artery leaving the systemic heart is the dorsal aorta. This thick-walled conduit passes a n t e r i o r l y , giving r i s e to v i s c e r a l branch vessels, and f i n a l l y s p l i t s into smaller a r t e r i e s which supply the arms, brain and other organs in the head region. In addition to the systemic heart, there are also two accessory hearts which raise the pressure of blood returning in the vena cava, in order to perfuse the g i l l s . From the g i l l s , blood i s directed back to the systemic heart through the g i l l e fferents. Thus, in cephalopods, the systemic and respiratory c i r c u l a t i o n s are arranged as two c i r c u i t s in series, and this i s analogous to the situation in mammals. In large specimens of Octopus d o f l e i n i (15 to 30 kg) Johansen and Martin (1962) found that the resting systemic heart rate was 8 to 18 beats per minute (at 7 to 9 degrees C ) , and the dorsal a o r t i c blood pressure varied from 45 to 70 cm of water in systole, with a pulse pressure of about 20 cm of water. Pressures in the g i l l afferent a r t e r i e s were somewhat lower, averaging about 15 cm of water in diastole and from 25 to 50 cm of water in systole (Johansen and Martin, 1962). Venous pressures were low (from 0 to 17 cm of water) and there is evidence that blood i s pumped against a pressure gradient from the small veins to the vena cava by active p e r i s t a l s i s of the veins (Smith, 1962). Pressure pulsations in the vena cava were in synchrony with, and l i k e l y a direct result of, respiratory pumping movements of 4 the muscular mantle (Johansen and Martin, 1962). Wells (1979, 1980) studied c i r c u l a t i o n in the much smaller and more active species, Octopus vulgaris, and observed heart rates of 40 to 50 beats per minute, while blood pressure in the dorsal aorta was about 40 cm of water in sytole and 15 cm of water in diastole (in 0.3 to 0.5 kg animals at 24 degrees C.) Recent measurements of the resting blood pressure in squids show the highest heart rates and the highest s y s t o l i c pressures, to date, in any cephalopod species (Bourne, 1982). This correlates well with the higher l e v e l of a c t i v i t y in squids compared to other cephalopods. In Loligo pealei the dorsal aort i c pressure ranged from 52 to 100 cm of water in peak systole, while the heart rate was about 90 beats per minute (in 0.1 to 0.2 kg animals at 20 degrees C ; Bourne, 1982). No information is available on the range of blood pressures or heart rates which might occur in much larger species of pelagic squids, or how their c i r c u l a t o r y system functions in periods of high a c t i v i t y . In the high pressure, closed c i r c u l a t o r y systems of mammals the passive e l a s t i c i t y of blood vessels is of fundamental importance (McDonald, 1974). The large a r t e r i e s of mammals are distended with blood during s y s t o l i c ejection, while positive blood flow to the peripheral vessels is maintained during diastole by e l a s t i c r e c o i l of these vessels. The highly p u l s a t i l e flow of blood from the heart is thus transformed to a r e l a t i v e l y steady flow through the exchange vessels. In their studies on the cephalopod 5 c i r c u l a t i o n , Johansen and Martin (1962) Wells (1979), and Bourne (1982) a l l pointed out that the ao r t i c pressure showed a gradual and asymptotic decline during d i a s t o l e , and they concluded that, as in mammals, the cephalopod aorta i s an e l a s t i c pressure reservoir which provides a pulse smoothing effect on the flow of blood to the peripheral vessels. Thus there is some evidence to suggest that e l a s t i c a r t e r i e s exist in cephalopods, and thi s raises an interesting question: What is the structural basis of thi s presumed e l a s t i c i t y ? In vertebrates, the rubber-like protein e l a s t i n i s responsible for the high e x t e n s i b i l i t y and e l a s t i c i t y of the artery wall under physiological pressures (McDonald, 1974). E l a s t i n , however, has been found exclusively in the vertebrates, and i t s appearance seems to coincide with the evolution of the advanced c i r c u l a t o r y systems in these animals (Sage, 1977). However, i t is not unlikely that other rubber-like proteins, similar to e l a s t i n should provide long-range e l a s t i c properties to blood vessels in cephalopods as well as in other invertebrates. H i s t o l o g i c a l studies have shown evidence for the presence of e l a s t i c ( i . e . , rubber-like) fibres in many invertebrate blood vessels, including cephalopod a r t e r i e s ( J u l l i e n et a l . , 1957, 1958; Elder, 1973), but in no case have these " e l a s t i c " f i b r e s , nor any invertebrate blood vessel, been subjected to di r e c t mechanical tests. I n i t i a l l y , the major goal of this study was to find, i s o l a t e and characterise the physical and chemical properties of the presumptive e l a s t i c component of cephalopod 6 a r t e r i e s , and by comparison with other protein rubbers, to gain some further understanding of the molecular basis for rubber-like e l a s t i c i t y in b i o l o g i c a l materials. The cephalopod used in t h i s research was the l o c a l "giant" P a c i f i c octopus, Octopus d o f l e i n i (Wulker), a species which occurs along the west coast of North America from Alaska to Mexico (Pickford, 1964). 0. d o f l e i n i was chosen because large specimens are readily available and they are e a s i l y maintained in c a p t i v i t y , and because the cardiovascular physiology has been studied in more d e t a i l in t h i s species than in any other cephalopod. In the study described here, a l l experiments were performed on the dorsal aorta of the octopus. In chapter II the structure of t h i s blood vessel i s investigated by histology and electron microscopy. A fibrous connective tissue component i s described which bears s t r i k i n g histochemical" and morphological s i m i l a r i t i e s to e l a s t i n f i b r e s in the vertebrate artery wall. Chapter III describes the i s o l a t i o n of the presumptive e l a s t i c fibres from the octopus artery wall. Mechanical and chemical tests demonstrate that these f i b r e s are composed of a protein with rubber-like properties, but one which can be distinguished from other known protein rubbers in several ways. Upon successful completion of the i n i t i a l objective of t h i s study, i t was of interest to test the hypotheses that the e l a s t i c f i b r e network in the octopus a r t e r i a l wall provides the basis for long-range e l a s t i c properties in this 7 blood vessel, and that t h i s , in turn, functions as a central e l a s t i c reservoir or "Windkessel" in the octopus a r t e r i a l c i rculat ion. Chapter IV i s an investigation of the s t a t i c and dynamic mechanical properties of the aorta of 0. d o f l e i n i . Results of these experiments show that t h i s vessel i s a highly d i s t e n s i b l e and e l a s t i c tube, which appears to be functionally equivalent to the aorta in vertebrates. Chapter V presents an analysis of cardiovascular dynamics of the octopus a r t e r i a l c i r c u l a t i o n , based on in vivo blood pressure and flow recordings, and predictions of hemodynamic c h a r a c t e r i s t i c s which can be made from the mechanical properties of the aorta. The results of t h i s investigation confirms that the a r t e r i a l c i r c u l a t i o n in 0. d o f l e i n i can be adequately described by a simple "Windkessel" model. F i n a l l y , in chapter VI, the results of Chapters II, III, IV and V are summarised. P a r a l l e l s between the mechanical properties of the c i r c u l a t o r y systems of cephalopods and vertebrates are discussed with regard to convergent evolution in these two groups of animals. 8 CHAPTER I I . THE STRUCTURE OF THE OCTOPUS AORTA A. INTRODUCTION It i s well known that vertebrate tissues which undergo large deformations, such as skin, lung and artery wall, have mechanical properties which are dependent on the p a r a l l e l arrangement of two fibrous connective tissue elements, e l a s t i n and collagen. The rubber-like protein e l a s t i n i s responsible for the high e x t e n s i b i l i t y and long-range e l a s t i c i t y under normal physiological stresses, while the s t i f f , r e l a t i v e l y inextensible collagen f i b r e s are recruited to provide the l i m i t i n g properties at high extensions (Bergel, 1972; Wainwright et a l . , 1976; Fung, 1981). Based on physical, chemical and u l t r a s t r u c t u r a l evidence, the existence of collagen in a l l metazoan phyla is well established (see reviews by Adams, 1978; Bornstein and Traub, 1979), but the occurrence of e l a s t i n in the invertebrates, u n t i l recently, has been in dispute. This uncertainty arose because the evidence presented was almost exclusively h i s t o l o g i c a l , and, depending on the methods chosen, various investigators have obtained c o n f l i c t i n g r esults (Argaud, 1908; Nutting, 1951; Anderson, 1954; Arvy, 1955; J u l l i e n et a l . , 1956; Bouillon and Vandermeersche, 1957; Van Gansen-Semal, 1960; Elder, 1966a,b) Sage (1977), conducted an extensive and systematic search for e l a s t i n in a wide variety of invertebrate tissues, including cephalopod a r t e r i e s . Her thorough chemical 9 analyses, in conjunction with staining properties, showed convincingly that e l a s t i n i s a protein unique to vertebrates. Sage concluded that the " e l a s t i c " fibres previously described in invertebrates are not e l a s t i n , but are probably functionally equivalent structures which, in general, w i l l react with e l a s t i n stains only after f i r s t being oxidised. Likewise, Elder and Owen (1967) and Elder (1973) found that invertebrate " e l a s t i c " f i b r e s could be demonstrated with t r a d i t i o n a l e l a s t i n stains only i f the tissues were f i r s t oxidised. Since oxidation i s also necessary for staining mammalian foetal " p r e - e l a s t i c " oxytalan f i b r e s with e l a s t i n stains, while mature e l a s t i n need not be pre-oxidised (Fullmer, 1960), i t has been suggested that invertebrates possess a form of phylogenetically incomplete or immature e l a s t i n , similar to oxytalan fibres (Elder, 1973; Garrone, 1981). However, no chemical evidence of any s i m i l a r i t y between e l a s t i n precursors and invertebrate presumptive e l a s t i c f i b r e s has yet been found. Presumptive e l a s t i c f i b r e s have been described in mollusc blood vessels in several h i s t o l o g i c a l studies. Wetekamp (1915) and J u l l i e n et a l . (1958) found an e l a s t i c f i b r e plexus in the c i r c u l a r muscle layer of the aorta of the pulmonate s n a i l Helix. Elder (1973) found concentric e l a s t i c lamellae in the a o r t i c bulb of the bivalve Mya arenaria, and in the dorsal aorta of the cephalopods Loligo pealei and Eledone cirrhosa. J u l l i e n et a l . (1957) described the mantle and tentacle a r t e r i e s and the dorsal aorta of the c u t t l e f i s h 10 Sepia o f f i c i n a l i s as having an internal e l a s t i c membrane and concentric medial e l a s t i c lamellae. They found this structure to be s t r i k i n g l y similar to the organisation of e l a s t i n in vertebrate a r t e r i e s . Similar observations have been made on the structure of aortae from the cephalopods Nautilus pompilius, Sepia latimanus, Sepioteuthis lessoniana and Nototodarus sloani (Gosline and Shadwick, 1982). The object of the present study was to examine the aorta of Octopus d o f l e i n i for h i s t o l o g i c a l l y i d e n t i f i a b l e " e l a s t i c " fibres and, in addition, to provide an ul t r a s t r u c t u r a l description of the aortic wall with emphasis on the connective tissue architecture. Barber and Graziadei (1965, 1966, 1967a,b) have reported on the fine structure of the aorta and other blood vessels in Octopus vulgaris. Although their description of the general structure of the art e r i e s i s probably applicable to 0. d o f l e i n i these workers have concentrated on d e t a i l s of blood vessel innervation and c a p i l l a r y structure with l i t t l e attention to connective t i ssues. 11 B. METHODS Live octopuses (0. d o f l e i n i ) were obtained from traps in Puget Sound, Washington, and from scuba divers in Barkley Sound off the west coast of Vancouver Island, B r i t i s h Columbia. Samples of the dorsal aorta were dissected from cold-anesthetised animals and prepared for l i g h t microscopy (L.M.), transmission electron microscopy (T.E.M.) and scanning electron microscopy (S.E.M.). For each technique some segments of aorta were prepared unpressurised while others were pressure-fixed at approximately the in vivo blood pressure (30 to 60 cm of water). For L.M., the tissues were fixed for 24 to 36 hours in Bouins f i x a t i v e , dehydrated in ethanol, cleared in xylene and embedded in paraf f i n wax. Sections cut at 5 to 8 um thickness were stained for e l a s t i c f i b r e s by the aldehyde fuchsin method of Cameron and Steele (1959) and counterstained with either picro-ponceau or orange G (Humason, 1972). For T.E.M., tissues were fixed for 2.5 hours at 4 degrees C. in 3% glutaraldehyde in 0.2M phosphate buffer at pH 7.4. Sucrose was added to the f i x a t i v e to give a f i n a l osmolarity of 1000 mOsm. The samples were then washed in buffer, post-fixed for 1 hour in a buffered 1% solution of osmium tetroxide, dehydrated in ethanol and embedded in epon 812 resin (Luft, 1961). Tissues were stained "en bloc" during dehydration with a saturated solution of uranyl acetate in 70% ethanol. Thin sections were cut with glass knives on 1 2 Porter-Blum MT1 and MT2 ultramicrotomes, mounted on carbon coated copper grids and stained with lead c i t r a t e . Sections were examined amd photographed on a Zeiss EM 10 microscope. In addition, 1 um thick sections of the epon embedded material were cut, mounted on glass and stained for l i g h t microscopy with 1% toluidine blue in 1% sodium borate. A Leitz Orthoplan microscope with automatic camera system was used for a l l h i s t o l o g i c a l examinations. For S.E.M., two preparatory techniques were employed. Some samples of aorta were quick-frozen in isopentane cooled in l i q u i d nitrogen, and then l y o p h i l i s e d . Other samples were fixed in buffered glutaraldehyde (described above) and dried by a c r i t i c a l point method (Boyde and Wood, 1969) using C02 as the t r a n s i t i o n a l l i q u i d . The dry samples were mounted on aluminum stubs, coated with a conducting layer of gold by vacuum evaporation, and viewed in a Cambridge Stereoscan microscope. 1 3 C. RESULTS 1. Histology Observations on p a r a f f i n and epoxy embedded material showed that the aorta of 0. d o f l e i n i i s very similar in structure to the aorta of 0. vulgaris (Barber and Graziadei, 1967b). There are f i v e d i s t i n c t tissue layers, as shown in Figures 2.1 and 2.2. Innermost i s an incomplete endothelium. The discontinuity of t h i s c e l l layer i s apparently common among molluscs, and has been reported previously in the blood vessels of cephalopods (Williams, 1902; Dahlgren and Kepner, 1908; Barber and Graziadei, 1965; Kawaguti, 1970; Browning, 1979) and gastropods (Tompa and Watabe, 1976; Curtis and Cowden, 1 9 7 9 ) . Unlike the continuous endothelium that l i n e s mammalian vessels, the endothelium in the octopus aorta can not function as a permeability barrier between the blood and artery wall. Beneath the endothelial c e l l s and l i n i n g the vessel lumen i s a fibrous layer, approximately 5 um thick, which is strongly reactive with aldehyde fuchsin. This layer is presumed to be e l a s t i c ( i . e . rubber-like) and w i l l be c a l l e d the internal e l a s t i c a (IE) by analogy to a similar structure in the a r t e r i e s of vertebrates (Stehbens, 1979). External to the IE i s a layer of c i r c u l a r l y oriented muscle fib r e s which make up about two thirds of the artery wall thickness. These muscles cannot be c a l l e d "smooth" because they have unusual c r o s s - s t r i a t i o n patterns (Fig. 2.2B,D), which have also been found in other cephalopod a r t e r i e s (Dahlgren and Kepner, 1908; Barber and Graziadei, 1967b) but 14 Figure 2 . 1 . Diagram of a transverse section of the dorsal aorta of 0 . d o f l e i n i , showing fiv e d i s t i n c t tissue layers. Facing-the lumen (L) i s an incomplete endothelial c e l l layer (e), which rests on the internal e l a s t i c a (IE). Outside t h i s i s a r e l a t i v e l y thick layer of c i r c u l a r muscle c e l l s (cm) which show cross s t r i a t i o n s . Outside t h i s i s a thinner layer of longitudinal muscle c e l l s (lm), and outermost i s a loose adventitia (ad) which contains collagen fibres ( c f ) , small blood vessels (bv) and nerve bundles (n). 15 Figure 2.2. Light micrographs of the octopus aorta. A) transverse section of the aorta showing the d i f f e r e n t tissue layers described in F i g . 2.1. Endothelial c e l l s appear to have been lost in the preparation. The internal e l a s t i c a i s i d e n t i f i e d by the positive reaction with aldehyde-fuchsin, while collagen is stained by picro-ponceau. The lumenal surface of the small blood vessel in the adventitia also stains with the aldehyde-fuchsin. B) Transverse section of the aorta, cut from an epon block and stained with toluidine blue. Endothelium i s present in t h i s preparation. The IE does not react p o s i t i v e l y with t h i s s t a i n . Note the s t r i a t i o n pattern in the c i r c u l a r muscles. C) A section of the aorta cut tangentially at the lumenal surface, showing a portion of the internal e l a s t i c a as a network of fibres with their major orientation in the long axis of the vessel. D) A high magnification view of the section shown in (B), to show d e t a i l s of the endothelial layer, the internal e l a s t i c a , and the unusual cross s t r i a t i o n s in the vascular muscle c e l l s , ad adventitia; bv small blood vessels; cf collagen f i b r e s ; cm c i r c u l a r muscles; e endothelium; IE internal e l a s t i c a ; L vessel lumen; lm longitudinal muscle. Scale bars: A,B = 100 um; C = 50 um; D = 10 um. 17 are not t y p i c a l of mollusc blood vessels in general (Tompa and Watabe, 1976; Curtis and Cowden, 1979). Outside the c i r c u l a r muscles i s a layer of long i t u d i n a l l y arranged muscle c e l l s . This i s surrounded by the outer tunic, or adventitia, a loosely organised layer of collagen f i b r e s . The adventitia also contains small blood vessels, which are probably part of a- vasa vasorum (Fig. 2.2A). Collagenous tissue, as indicated by the picro-ponceau stain, i s also found in small patches in the outer portion of the c i r c u l a r muscle layer (Fig. 2.2A). The p o s s i b i l i t y that the IE may provide e l a s t i c i t y in the artery wall makes the organisation of the fibres in the IE p a r t i c u l a r l y interesting. Figure 2.2C shows that, in the unpressurised aorta, the presumptive e l a s t i c fibres are about 2 to 5 um in diameter, and l i e e s s e n t i a l l y p a r a l l e l to the long axis of the vessel. This observation i s confirmed by the S.E.M. pictures (Fig. 2.3A). A number of ovoid endothelial c e l l s about 10 um long are also seen (Fig. 2.3B, C). When the aorta i s fixed at physiological pressures (30 to 60 cm of water) the_ IE i s stretched in the circumferential and longitudinal directions at the same time (since the artery lengthened when i t was i n f l a t e d ) ; the longitudinal f i b r e s of the IE separate and l a t e r a l connections between the fi b r e s are v i s i b l e (Fig. 2.3B,C). At the higher of the two pressures the fibres have a "taut" appearance and l i e with more d i s t i n c t l y p a r a l l e l orientation (Fig. 2.3C) than those at the lower pressure. This gives the impression that the fib r e s 18 Figure 2.3. Scanning electron micrographs of the lumenal surface of the octopus aorta, showing the fibres of the internal e l a s t i c a . Arrows in the l e f t margin indicate the longitudinal axis of the vessel. A) The lumenal surface of the aorta (lower portion of the figure) meeting the transversely cut c i r c u l a r muscle layer (upper portion of the f i g u r e ) . The IE appears as a sheet of fibres with orientation in the longitudinal d i r e c t i o n . Fixed unpressurised, freeze dried. B) The lumenal surface of an aorta fixed at 30 cm of water pressure. The fibres of the IE retain their predominantly longitudinal orientation, but separate l a t e r a l l y with the increase in circumference to reveal l a t e r a l connections between f i b r e s (arrows). C r i t i c a l point dried. C) Lumenal surface of an aorta fixed at 60 cm of water pressure. The fibres appear to be stretched taut, and have a more d i s t i n c t l y p a r a l l e l orientation. Lateral connections are again v i s i b l e (arrows). C r i t i c a l point dried. cm c i r c u l a r muscle; e endothelial c e l l ; IE internal e l a s t i c a ; l c l a t e r a l connections. Scale bars: A = 20 um; B = 10 um. 19 20 bear a greater tension with increased pressure. Thus, i t i s suggested that the IE i s as a contiguous sheet of long e l a s t i c f i b r e s which l i n e s the vessel lumen, and which presumably provides mechanical reinforcement to the artery wall in both longitudinal and circumferential d i r e c t i o n s . The morphological structure of the IE shown in Figure 2.3 i s remarkable in i t s s i m i l a r i t y to the internal e l a s t i c a of mammalian veins. In the canine saphenous vein l o n g i t u d i n a l l y oriented e l a s t i n f i b r e s , 1 to 2 um in diameter, are joined by much thinner l a t e r a l extensions into a continuous network which forms the internal e l a s t i c lamina (Crissman et a l . , 1980). 2) Ultrastructure The IE and underlying c i r c u l a r muscle layers are shown in electron micrographs of transverse and longitudinal sections of the artery (Fig. 2.4, 2.5, 2.6A). The IE appears as an amorphous material of low electron density which contains a f i b r i l l a r component, aligned p a r a l l e l to the long axis of the artery. These f i b r i l s are aggregates of 25nm wide filaments which stain more densely than the amorphous material (Fig. 2.6A). In addition, fine " e l a s t i c " f i bres (150 to 400 nm in diameter) arise from the amorphous portion of the IE and traverse into the artery wall between muscle c e l l s (Fig. 2.4, 2.5B). A network of similar amorphous material (which may be continuous with the IE) is found throughout the c i r c u l a r and longitudinal muscle layers (Fig. 2.6B, 2.7). These observations provide good evidence that an extensive 21 Figure 2.4. Electron micrograph of a longitudinal section of the octopus aorta, fixed under no distending pressure. When deflated, the aorta has many circumferential folds in the inner wall. This section i s taken at one such fo l d , as indicated by the inset diagram. The IE i s seen as a layer of amorphous material containing dense f i b r i l s which l i e in the di r e c t i o n of the long axis. These f i b r i l s are aggregates of 25 nm wide filaments. Presumptive fine e l a s t i c f ibres arise as projections of the amorphous component of the IE and run between the c i r c u l a r muscle c e l l s . a amorphous component of the IE; cm c i r c u l a r muscle; e endothelial c e l l ; d electron dense area in cm; f f i b r i l l a r component of the IE; fe fine e l a s t i c f i b r e s . 22 23 Figure 2.5. Electron micrographs of the octopus aorta. A) Transverse section near the vessel lumen. B) Longitudinal section at the boundary of the IE and the c i r c u l a r muscle layer. Fine e l a s t i c fibres from the amorphous portion of the IE project into the muscle layer. Dense areas resembling hemidesmosomes may be s i t e s of attachment of these fibres to the muscle c e l l s . Thick and thin filaments are seen within the muscle c e l l s , a amorphous component of the IE; d electron dense area in muscle c e l l ; f f i b r i l l a r component of the IE; fe fine e l a s t i c f i b r e s ; h hemidesmosome-1ike areas; tk thick myofilaments; tn thin myofilaments. Scale bars: A = 2 um; B = 500 nm. 2U 25 Figure 2.6. A) Longitudinal section of the IE showing the amorphous and f i b r i l l a r components at high magnification. The f i b r i l s are aggregates of 25 nm wide filaments . B) Longitudinal section of the central portion of the c i r c u l a r muscle layer in the aorta. A network of amorphous connective tissue i s seen in the spaces between muscle c e l l s (arrows). This may be an extension of the fine e l a s t i c f i b r e s which arise from the IE (Fig. 2.4, 2.5). Scale bars: A = 1 um; B = 3 um. 2 6 27 Figure 2.7 A) Transverse sections of the longitudinal muscle layer in the aorta. An amorphous i n t e r c e l l u l a r connective tissue component, which may be continuous with the intermuscular projections of the internal e l a s t i c a seen in Fig.2.4, 2.5) i s prominant in t h i s region (arrows). B) A higher magnification view of the section in (A). Hemidesmosome-like areas are seen in the muscle c e l l s adjacent to the e l a s t i c f i b r e (arrows). fe fine e l a s t i c f i b r e s ; cm c i r c u l a r muscle c e l l ; lm longitudinal muscle c e l l ; tk thick myofilaments. Scale bars: A = 2 um; B = 1 um. 28 29 array of e x t r a - c e l l u l a r e l a s t i c fibres i s present, not only at the lumenal surface, but also throughout the artery wall. If these fibres are indeed e l a s t i c then t h i s network might be mechanically analogous to the array of e l a s t i n lamellae found in the tunica media of vertebrate a r t e r i e s (Stehbens, 1979), and therefore could be responsible for supporting much of the t e n s i l e load which the artery wall i s subjected to in the physiological range of pressures. The i n t e r - c e l l u l a r fibres may be linked to the muscle c e l l s at s i t e s where dense areas, resembling hemidesmosomes, are found (Fig. 2.5B, 2.7B). The muscle c e l l s contain thick filaments which vary from 30 to 40 nm in diameter (Fig. 2.4, 2.5, 2.7). Thin filaments are discernable in some sections and are about 8 nm in diameter (Fig. 2.5B). In addition, the c i r c u l a r muscle c e l l s contain patches of electron dense material which may be attachment s i t e s for the myofilaments, similar to Z bands (Fig. 2.4, 2.5), and which give r i s e to the unusual pattern of s t r i a t i o n s seen in the l i g h t micrographs (Fig.2.2). Figure 2.8A shows that in the unpressurised artery the bundles of collagen fibres which form the a d v e n t i t i a l layer are loosely organised, with no apparent preferred orientaton. These fibres have a major a x i a l p e r i o d i c i t y of 60 to 64 nm (Fig. 2.8B), which i s similar to the pattern seen in squid mantle collagen (Hunt et a l . , 1970) and in v i r t u a l l y a l l vertebrate collagens (Bornstein and Traub, 1979). Some small areas of collagen fibres are also seen in the outer portion 30 of the c i r c u l a r muscle l a y e r , as shown, i n F i g u r e 2.8C. By comparing F i g u r e 2.8 to F i g u r e s 2.5 and 2.6 i t seems c l e a r that the presumptive e l a s t i c m a t e r i a l , with i t s rather amorphous appearance i s e a s i l y d i s t i n g u i s h e d from the s t r i a t e d c o l l a g e n f i b r e s , which are found p r i m a r i l y i n the advent i t i a . 31 Figure 2.8. A) collagen fibres in the adventitia of the aorta. Bundles of nerve axons are also seen throughout. B) Collagen f i b r e s from the adventitia showing an a x i a l banding pattern of about 64 nm (arrows). C) Collagen fibres in the outer portion of the c i r c u l a r muscle layer, ax axons; cf collagen f i b r e s ; cm c i r c u l a r muscles. Scale bars: A = 2 um; B =100 nm; C =2 um.12=12 32 33 D. DISCUSSION Prior to this study, several reports have .claimed to demonstrate the existence of e l a s t i c f i b r e s in mollusc blood vessels (Wetekamp, 1915; J u l l i e n et al.,1957, 1958; Elder 1973). This i s the f i r s t u l t r a s t r u c t u r a l investigation which describes a network of non-collagenous connective tissue fibres throughout the wall of a cephalopod artery. Certain h i s t o l o g i c a l and morphological features suggest that these fibres are e l a s t i c , i . e . rubber-like, and therefore may be analogous to vertebrate e l a s t i c f i b r e s . The positive staining reaction with aldehyde-fuchsin was used as the i n i t i a l c r i t e r i o n by which the internal e l a s t i c a (IE) was defined in the octopus aorta. Aldehyde-fuchsin i s one of many stains used to d i f f e r e n t i a t e e l a s t i c f i b r e s from collagen in vertebrate tissues (Fullmer, 1965), but the major component of vertebrate e l a s t i c fibres is e l a s t i n , a protein which i s absent from invertebrates (Sage, 1977). What then i s the rationale for using e l a s t i n stains to search for " e l a s t i c " f i bres in invertebrates? Since v i r t u a l l y nothing i s known about the chemical properties of any presumptive e l a s t i c f i b r e s from invertebrates, no alter n a t i v e to the vertebrate stains can yet be proposed. Therefore, i n i t i a l investigations are based on the assumption that i f connective tissue fibres which are mechanically analogous to e l a s t i n exist in invertebrates, they may have some histochemical s i m i l a r i t i e s to e l a s t i n . 34 As i s the case for many h i s t o l o g i c a l techniques the exact structure and staining mechanism of aldehyde-fuchsin is uncertain. It is thought to be a mixture of N-ethylated derivatives of pararosanilin (=basic fuchsin) which react with aldehyde groups on the e l a s t i n protein (Horobin and James, 1970; Horobin and Flemming, 1980; Puchtler and Waldrop, 1979). However, a necessary step in the •aldehyde-fuchsin technique for e l a s t i n , as well as for the invertebrate f i b r e s , i s oxidation of the tissue with a c i d i f i e d permanganate prior to staining (Elder and Owen, 1967; Elder, 1973; Bock, 1977). Currently, i t i s thought that oxidative cleavage of the desmosine cross - l i n k s in e l a s t i n produces lysine-derived aldehydes which are free to react with the stain (Rudell, 1969; Fischer, 1979). Presumably the aldehyde-fuchsin reaction with invertebrate " e l a s t i c " f i b r e s , including the IE of the octopus aorta, i s also based on permanganate inducible aldehydes. It is possible that these aldehydes may be derived from lysine residues in a cross-link structure. However, th i s does not suggest the presence of desmosine cross-links in invertebrate f i b r e s ; indeed Sage (1977) has shown that desmosine i s absent from the invertebrate phyla. Orcein, resorcin-fuchsin and iron-hematoxylin are stains which react with e l a s t i n by mechanisms not requiring prior oxidation of the tissue (Horobin and Flemming, 1980; Puchtler and Waldrop, 1979). However, these stains give negative results when used on the aorta of 0. d o f l e i n i (this 35 study) as we l l as with other i n v e r t e b r a t e " e l a s t i c " f i b r e s that have been i d e n t i f i e d by the al d e h y d e - f u c h s i n or s p i r i t - b l u e techniques (Argaud, 1908; J u l l i e n et a l . 1956; E l d e r and Owen, 1967). Thus, p r e - o x i d a t i o n of the t i s s u e appears to be a r e q u i r e d step i n s t a i n i n g presumptive e l a s t i c f i b r e s i n the octopus and other i n v e r t e b r a t e s . The negative r e s u l t s with some of the e l a s t i n s t a i n s , when used on i n v e r t e b r a t e t i s s u e s , has l e d to c o n f l i c t i n g o p i n i o n s on the e x i s t e n c e of e l a s t i n or e l a s t i c f i b r e s i n the i n v e r t e b r a t e s (see E l d e r and Owen, 1967). Based on the work of Sage (1977), we now know that the e l a s t i n p r o t e i n i s unique to v e r t e b r a t e s , but i t seems l i k e l y that there are a v a r i e t y of other r u b b e r - l i k e p r o t e i n s throughout the many i n v e r t e b r a t e p h y l a . Observations by e l e c t r o n microscopy support the presumption that the f i b r e s demonstrated by al d e h y d e - f u c h s i n in the octopus aorta are indeed an e l a s t i c m a t e r i a l . What i s d e s c r i b e d here as the i n t e r n a l e l a s t i c a i n 0. d o f l e i n i i s undoubtedly e q u i v a l e n t to the s t r u c t u r e p r e v i o u s l y d e s c r i b e d as a "basement membrane" i n the a o r t a of 0. v u l g a r i s (Barber and G r a z i a d e i , 1967b). Although the IE may act as a supp o r t i n g membrane f o r the d i s c o n t i n u o u s l a y e r of e n d o t h e l i a l c e l l s , i t s appearance as a mechanically continuous network of f i b r e s i n the i n f l a t e d a r t e r y i s s t r o n g l y suggestive of a loa d bearing s t r u c t u r e . In the small e r blood v e s s e l s of v e r t e b r a t e s there i s a complete r e t i c u l a r basement membrane between the endothelium and 36 i n t e r n a l e l a s t i c a , but i n the l a r g e a r t e r i e s the true basement membrane i s o f t e n fragmented or absent and the e l a s t i c l a y e r becomes the f u n c t i o n a l basement membrane (Pease and M o l i n a r i , 1960; Stehbens, 1979). Therefore i t i s not unreasonable to suggest that i n the octopus a o r t a the e n d o t h e l i a l c e l l s l i e d i r e c t l y on a l a y e r of e l a s t i c f i b r e s . The s c a r c i t y of e n d o t h e l i a l c e l l s i n the a o r t a might be due, i n p a r t , to damage du r i n g p r e p a r a t i o n , but i t seems l i k e l y that i n v i v o t h i s c e l l l a y e r i s an incomplete one, as i s t y p i c a l l y seen in molluscan blood v e s s e l s (see C u r t i s and Cowden, 1979). Recently, Browning (1980) has p r o v i d e d d e t a i l s of the lumenal surface topography in the blood v e s s e l s of Octopus p a l l i d u s , from v a s c u l a r c o r r o s i o n c a s t s . His r e s u l t s show that the lumenal s u r f a c e of l a r g e a r t e r i e s has l o n g i t u d i n a l r i d g e s about 2 to 5 um wide; these undoubtedly correspond to the f i b r e s of the IE. In a d d i t i o n , Browning's c a s t s i n d i c a t e that e n d o t h e l i a l c e l l s (10 to 15 um long) are widely s c a t t e r e d , j u s t as shown in the a o r t a of 0. d o f l e i n i ( F i g u r e 2.3B). U l t r a s f c u c t u r a l l y the s i m i l a r i t i e s between the IE of the octopus a o r t a and v e r t e b r a t e e l a s t i c f i b r e s are s t r i k i n g . The IE f i b r e s are p r i m a r i l y an amorphous m a t e r i a l which c o n t a i n s a small amount of more densely s t a i n i n g f i b r i l s . S i m i l a r l y , i n v e r t e b r a t e blood v e s s e l s the e l a s t i c f i b r e s have two m o r p h o l o g i c a l l y d i s t i n c t c o n s t i t u e n t s . The major c e n t r a l region i s the amorphous p r o t e i n - r u b b e r e l a s t i n ; at the p e r i p h e r y are the g l y c o p r o t e i n " m i c r o f i b r i l s " , which are 37 around 10 nm in diameter (Ross and Bornstein, 1969). The m i c r o f i b r i l s are thought to be l a i d down in embryogenesis to provide a framework on which to build the e l a s t i n network (Greenlee et a l . , 1966; Ross and Bornstein, 1969). It i s proposed here that the amorphous component of the IE in the octopus aorta is a rubbery protein, l i k e e l a s t i n , and that the f i b r i l l a r component i s analogous to the vertebrate m i c r o f i b r i l s and likewise may play a role in the morphogenesis of the IE f i b r e s . In addition to the IE, intermuscular presumptive e l a s t i c f i b r e s have been demonstrated in the octopus aorta. Although no single f i b r e has been followed through the entire wall thickness, the presence of these amorphous fibres in a l l parts of the c i r c u l a r and longitudinal muscle layers, and the observation that in sections adjacent to the vessel lumen the fibres a r i s e from the IE, leads to the conclusion that the presumptive e l a s t i c f i b r e s form a mechanically continuous network throughout the artery wall. These intermuscular fibres also stain with aldehyde-fuchsin but due to their small size (150 to 400 nm) they are v i s i b l e only at the highest magnification of the l i g h t microscope, and are not seen in Figure 2.2A. This is in contrast to reports on blood vessels from other cephalopods in which e l a s t i c fibres are seen as thick concentric lamellae ( J u l l i e n et a l . , 1957; Elder, 1973; Gosline and Shadwick, 1982). In vertebrate a r t e r i e s the e l a s t i c f i b r e s are also arranged in concentric lamellae (each about 10 um thick) 38 interspersed with muscle c e l l s . Fine e l a s t i n f i b r i l s l i n k the lamellae together, thus forming a continuous network around the muscle c e l l s . Further mechanical s t a b i l i t y i s provided by fusion of the muscle c e l l s to the lamellae (Pease and Paul, 1960; Wolinsky and Glagov, 1964). The apparent linkage between muscle c e l l s and intermuscular fibres seen in Figures 2.5 and 2.7 may serve a similar function in the octopus aorta. It seems that the major structural difference between the octopus and vertebrate aortae i s the size, and abundance, of the intermuscular e l a s t i c f i b r e s . In mammals e l a s t i n comprises 30 to 40% of the aortic wall (Burton, 1954; Stehbens, 1979). In contrast, the wall of the octopus aorta is primarily muscle c e l l s , and the presumptive e l a s t i c f i b r e system i s a minor component. If indeed the octopus " e l a s t i c " fibres are mechanically similar to e l a s t i n , then the r e l a t i v e l y small quantity of these fibres in the octopus aorta, compared to the large proportion of e l a s t i n in mammalian aortae, may simply r e f l e c t the fact that the blood pressure which the fibres must support i s much lower in the cephalopod than in the mammal. 39 CHAPTER II I . CHEMICAL AND MECHANICAL PROPERTIES OF OCTOPUS ELASTIC FIBRES A. INTRODUCTION In the previous chapter, an examination of the aorta of Octopus d o f l e i n i by l i g h t and electron microscopy revealed the presence of a network of presumptive e l a s t i c f i b r e s . It was proposed that the function of these fibres is to give long range e l a s t i c properties to the wall of the blood vessel, just as the rubber-like protein e l a s t i n does in the ar t e r i e s of vertebrates. Other h i s t o l o g i c a l studies have claimed to demonstrate that e l a s t i c (rubber-like) fibres occur in the blood vessels of many invertebrates (see Elder, 1973), but in no case have the presumptive e l a s t i c fibres been isolated and tested mechanically. The purpose of this study was to test the hypothesis that the " e l a s t i c " fibres in the octopus aorta are indeed composed of a rubber-like protein, by di r e c t chemical and mechanical analyses of isolated native and p u r i f i e d samples of the f i b r e network. By using the kinetic theory of rubber e l a s t i c i t y as a model for these experiments, i t should be possible to gain some understanding of the molecular basis for rubber-like e l a s t i c i t y in this previously undescribed protein. The elegant work by Weis-Fogh (1961a, b) on the insect protein-rubber r e s i l i n , and a recent study on the physical properties of single e l a s t i n fibres (Aaron and Gosline, 1981) provide the framework on which much of the present work is based. 40 B. RUBBER ELASTICITY 1. Network Properties The kinetic theory of rubber e l a s t i c i t y i s a mathematical description of the long-range e l a s t i c properties of rubber-like polymers (Treloar 1975). This theory considers the molecular structure as an ideal one characterised by the following i m p l i c i t features. 1) The material i s composed of f l e x i b l e long-chain polymeric molecules. 2) These molecules are joined together by permanent cross-links into an isotropic three-dimensional network. 3) The molecular chains between cross-links are k i n e t i c a l l y free and in constant motion due to thermal a g i t a t i o n . Each chain i s a set of "random l i n k s " that, with the freedom to rotate r e l a t i v e to each other, tend to take up the s t a t i s t i c a l l y most probable conformations (Treloar, 1975). When the material is strained the network is distorted, thereby forcing the molecular chains to adopt new conformations of lower p r o b a b i l i t y than in the unstrained state. In other words the conformational entropy of the network i s decreased with increasing deformation. The e l a s t i c restoring force then arises from the tendancy of the molecular chains to spontaneously return to the state of higher entropy, i . e . the unstrained dimensions. Thus, in theory, extension of a rubber-like polymer is associated with a decrease in the conformational entropy of the network, with no corresponding change in internal energy. In contrast, 41 extension of a r i g i d s o l i d , such as s t e e l , i s associated with di r e c t d i s t o r t i o n of chemical bonds. In th i s case the e l a s t i c force arises from a change in internal energy rather than a change in entropy. The kinetic thoery of rubber e l a s t i c i t y provides a s t a t i s t i c a l treatment of long chain polymer molecules which has been used to quantify the network properties of rubber-like proteins. This model ide a l i s e s each molecular chain between crosslinks as a set of (s) thermally agitated random l i n k s , each of length (1) (see F i g . 3.1). The conformation of the molecular chains can be represented by a random walk with the number of steps between the two ends being equal to the number of l i n k s (s). The distance which separates the chain ends i s ( r ) , while the f u l l y extended length would be ( s l ) . If the number of lin k s (s) is r e l a t i v e l y large, and the end to end separation (r) is much less than the chain length ( s l ) , i . e . the rotational freedom is preserved, then the d i s t r i b u t i o n of (r) values closely f i t s a Gaussian p r o b a b i l i t y function. The root-mean-square value of (r) is given by ( s l ) (Treloar, 1975). When a single chain is deformed by an external force, (r) i s altered, and the Gaussian s t a t i s t i c s provide a basis for c a l c u l a t i n g the associated change in entropy of the molecule. Assuming that the internal energy remains constant, then the e l a s t i c force arises from the entropy change and i s d i r e c t l y proportional to the degree of deformation of the chains. t X Figure 3.1. The idealised random c o i l molecule. The conformation of the molecular chain i s represented by a random walk of (s) steps, each of length, 1. The extended chain length i s ( s x l ) , the folded length i s r, the distance from the o r i g i n , 0, to the point P. 43 Clearly, complete rotational freedom at the covalent bonds in real molecules cannot be achieved because of physical r e s t r i c t i o n s . In proteins, only the single bonds to the alpha carbon are free to rotate, while the peptide bond i s fixed and cannot rotate (Dickerson and Geis, 1969). Large side groups on the amino acids w i l l reduce the rotational freedom of a protein molecule. In the p r a c t i c a l application of the kinetic theory to a real molecule such as rubber or a rubber-like protein i t i s necessary to replace the concept of an ideal random link by "functional" random l i n k . This may be defined as a segment of the chain containing enough bonds with p a r t i a l -rotational freedom which together have e s s e n t i a l l y the same kinetic freedom as the ideal random l i n k . Now, applying the kinetic theory to a cross-linked isotropic network of random-link molecules, we have the following relationship between un i d i r e c t i o n a l force and extension: (T= NkT ( fr- or2") (3.1) where § i s the nominal stress, defined as t e n s i l e force per unit of unstrained cross-sectional area, N is the number of chains per unit volume of material (an indication of cross-link density), k is the Boltzman constant, 1.38 X 10 2 3 Joules/molecule degree, T i s the absolute temperature, and ^ i s the extension r a t i o , defined as the extended length divided by the unstrained length (therefore 44 (T= 0 when cL= 1 .0) . This equation adequately describes the behaviour of rubber-like polymers in the dry state. However, protein-rubbers are s t i f f , glassy materials when dry (Gosline, 1980). Strong peptide-peptide hydrogen bonds between the folded chains render the network immobile. Polar solvents, l i k e water, swell the protein by competing for the peptide hydrogen bond s i t e s and thus allow the molecular chains to become k i n e t i c a l l y free and random. In th i s swollen state proteins l i k e e l a s t i n , r e s i l i n and abductin become rubber-like (Gosline, 1978a; Weis-Fogh, 1961a; Alexander, 1966) . The kinetic theory i s modified to deal with i s o t r o p i c a l l y swollen rubbers, by introducing a term for the volume fraction,v, in the form: _-' = NkT vVs ( \ - X~ a) (3.2) where cr' i s now the nominal stress based on the swollen unstrained cross-sectional area. The volume f r a c t i o n , v, i s the r a t i o of unswollen to swollen volumes, and X i s the extension r a t i o based on swollen dimensions ( i . e . X = (Av Y 3 ). This equation has been used to describe the e l a s t i c properties of the water-swollen protein-rubbers r e s i l i n and e l a s t i n (Weis-Fogh, 1961b; Aaron and Gosline, 1981), and w i l l be used as a model in the following analysis of the 45 mechanical properties of the presumptive e l a s t i c fibres from the octopus aorta. A rubber can be characterised by a single material constant c a l l e d the e l a s t i c modulus G (Treloar, 1975), given as: G = NkT = pRT/Mc (3.3) where G i s a measure of the s t i f f n e s s of the material and i s given in N/m and £> i s the density of the dry polymer (for protein ^ = 1.33 g / c c ) . R i s the gas constant, 8.31 Joules/mole degree. Mc i s the average molecular weight of the chains between c r o s s - l i n k s . cj ' and >\ can be determined experimentally from force extension tests, and Gv x / 3 can be calculated from the slope of a plot of CJ' vs. (X - ^  7~) . To obtain G, v must be known. In addition, equation 3.3 can be used to calculate the molecular weight between cr o s s - l i n k s , Mc. This equation also shows that a decrease in Mc, i . e . an increase in the cross-link density, w i l l result in a proportional increase in the modulus. Thus the ideal (Gaussian) rubber i s characterised by i t s modulus, G, which simply depends on the number of cross-linked chains in a unit volume of material. S t i f f e l a s t i c solids are usually described by the Young's modulus, Y, defined as the i n i t i a l slope of a plot of C vs. )> for the material. This i s equivalent to the spring constant for a Hookean ( l i n e a r l y e l a s t i c ) body. S i m i l a r l y , Y 46 can be obtained for a rubber as: Y = d (T /d X (3.4) The theory so far described is for a rubber-like polymer whose molecular chains are very long so that r/sl<<1, where r i s the distance between the ends of the folded chain (see F i g . 3.1). In r e a l i t y the Gaussian predictions work only for r e l a t i v e l y small extensions. As \ increases, r also increases so r / s l eventually approaches a value of 1.0. This means the chains are being pulled out from their random-coil conformation to one that i s less able to accomodate further deformation. The network e f f e c t i v e l y becomes s t i f f e r the further i t i s extended, and the observed stress values exceed what i s predicted by the Gaussian theory. Treloar (1975) has developed a non-Gaussian model which takes into account the f i n i t e e x t e n s i b i l i t y of chains in real networks. The form of the non-Gaussian curve i s highly dependent on the number of random l i n k s , s, and i s given by the following series expansion as applied to swollen networks: 0"' = G v / 3 ( X - V ^ ) [1 + ( 3 / 2 5 s ) ( 3 V + 4/>0 + 297/61 25s 1 (5>\4+ 8A + Q/>\ ) + 1 231 2/2205000s3 (35>f+ 60V+ 72 + 64 / A ? ) + 1 26 1 77/( 693 ( 673750 ) sH ) (630 >\ + 1120>f+ 1440>l+ 1536A+ 1280 /A 4 ) + . . . ] (3.5) Note that this approximates to the Gaussian form (eqn. 3.2) when s i s very large, or when the extension, A , i s very 47 small. By comparing force-extension data to plots of equation 3.5 an estimate of s can be obtained. The quantity s i s important because i t i s a measure of the f l e x i b i l i t y of the molecular chains, and an indication of the influence of the non-Gaussian effects on the network. Thus, the two parameters s and G are necessary to describe the e l a s t i c properties of real rubber-like materials. 2. Thermoelasticity As stated above, deformation of an ideal rubber causes a decrease in the conformational entropy of the molecular network, with no associated change in internal energy. The e l a s t i c restoring force arises solely due to the change in entropy. Equation 3.1 predicts that the e l a s t i c force for a rubber w i l l increase in proportion . to the absolute temperature (in contrast, s t i f f e l a s t i c s olids which- exhibit bond energy e l a s t i c i t y become s l i g h t l y more deformable with increased temperature). This suggests a simple experiment to test the r e l a t i v e contribution of entropy changes to the e l a s t i c properties of a material. A sample i s stretched and held at a constant length while the e l a s t i c force i s measured as a function of temperature. For this experiment the following thermodynamic equation applies (Flory, 1953): f = (dH/dL) - T(dS/dL) (3.6) T,P T,P where f = the e l a s t i c force, H = the enthalpy, L = the length of the sample, T = the absolute temperature, S = the 48 entropy and P = the p r e s s u r e . T h i s equation s t a t e s that the e l a s t i c f o r c e i s composed of enthalpy and entropy components. These components can be measured using the f o l l o w i n g r e l a t i o n s h i p ( F l o r y , 1953): -(dS/dL) = (df/dT) ( 3 , 7 ) T,P L,P which, s u b s t i t u t e d i n t o eqn. 3.6 g i v e s : f = (dH/dL) + T(df/dT) (3.8) T,P L,P From eqn. 3.8 we see that the slope of the i s o m e t r i c force-temperature curve, i . e . ( d f / d T ) L , P , g i v e s the e n t r o p i c component while the i n t e r c e p t at T = 0 degrees K. (by l i n e a r e x t r a p o l a t i o n ) w i l l be the e n t h a l p i c component. However, the k i n e t i c theory of rubber e l a s t i c i t y p r e d i c t s that the change in i n t e r n a l energy, U, of the network deformed at constant volume w i l l be zero, i . e . (dU/dL)T,V = 0. Only under c o n d i t i o n s of constant volume w i l l the enthalpy change be equal to the i n t e r n a l energy change; the l a t t e r being the q u a n t i t y r e q u i r e d to t e s t the k i n e t i c t heory. For unswollen rubbers thermal expansion i s r e l a t i v e l y s m a l l , but f o r water swollen p r o t e i n - r u b b e r s there may be l a r g e volume changes with temperature due to movement of water i n t o or out of the network ( G o s l i n e , 1980). In t h i s case (dH/dL)T,P w i l l not j u s t be the i n t e r n a l energy change a s s o c i a t e d with the conformation of the molecule, but w i l l 49 also have an energy component associated with the mixing of the water and protein (Gosline, 1980). For e l a s t i n stretched in water (dU/dL)T,V i s close to zero ( M i s t r a l i et a l . , 1971; Dorrington and McCrum, 1977), but (dH/dL)T,P is large and negative. It appears that the necessary internal energy term can only be obtained i f the thermoelastic experiment i s done at constant volume. This condition may be approximated by minimising the swelling changes, for example, with the use of appropriate solvent mixtures (Hoeve and Flory, 1958), pH (Weis-Fogh, 1961a), or by testing the hydrated sample as a closed system, i . e . immersed in o i l (Gosline, 1980). A very p r a c t i c a l alternative to trying to maintain constant volume is to test the sample as an open system, described by equation 3.6, and then to make corrections to the data to account for the swelling changes (Dorrington and McCrum, 1977). This involves transforming the force - temperature plots from constant length to constant extension r a t i o (A) . Assuming that swelling i s iso t r o p i c , this procedure corrects to constant volume. Under these conditions the following equations w i l l apply (Flory, 1953): f = (dU/dL) T(dS/dL) (3.9) T,V T,V and -(dS/dL) (df/dT) (3.10) T,V P,> which together y i e l d : f « (dU/dL) + T(df/dT) (3.11) T,V 50 which i s analogous to eqn. 3.8. Now the slope of the force temperature plot at constant X gives the desired entropy change -(dS/dL)T,V, and the intercept at T = 0 degrees K. is the internal energy change (dU/dL)T,V associated solely with the orientation of the molecular chains. Figure 3.2A shows force - temperature plots for isoprene rubber corrected to constant ?\. In Figure 3.2B the force - extension curve at 20 degrees C. is plotted along with the internal energy and entropy components obtained by application of equations 3.10 and 3.11 to the data in Figure 3.2A. As predicted by the kinetic theory, (dU/dL)T,V i s very close to zero except at high extensions where strain-induced c r y s t a l l i s a t i o n occurs. 51 T(0C) Figure 3.2. A) Force-temperature plots for natural isoprene rubber, corrected to constant extension r a t i o . B) Force-extension curve for natural rubber derived from the data in (A). f=force, S=entropy, U=internal energy, <* = extension r a t i o . 52 C. METHODS 1. Composition of the Artery Wall a. Water content. Fresh samples of aorta were cut up with a razor blade, blotted, weighed and dried on aluminum f o i l at 60 degrees C. Dry weights were determined after 12, 16 and 36 hours. b. E l a s t i c f i b r e content. The dry samples from (a) were transferred to 15 ml glass centrifuge tubes and powdered with a teflon tissue homogeniser. Each tube then received 8 ml of 98% formic acid and was shaken vigorously on a vortex mixer. The samples were l e f t in acid for periods of 6, 18, 24, 48, and 72 hours with continuous a g i t a t i o n . The tubes were then spun in a Sorvall RC2-B centrifuge at T2,000Xg for 20 minutes. The supernatant was poured off, and the p e l l e t s were re-suspended in water and washed several times u n t i l no odour of formic acid could be detected. The tubes were l e f t overnight with the f i n a l water rinse and the contents then dried at 60 degrees C. to constant weight. This insoluble residue represents the portion of artery wall that i s insoluble in water and formic acid, and is in fact a very pure preparation of the e l a s t i c f i b r e protein (see amino acid analysis below). The extraction, washing, drying and weighing procedures were a l l ca r r i e d in the same centrifuge tubes to eliminate transfer steps and minimise loss of the residue. The use of formic 53 acid here i s based on techniques used for e l a s t i n extraction and p u r i f i c a t i o n (Steven et a l . , 1974; Rasmussen et a l . , 1975). Another method used was extraction of the aorta in 6M guanidine HC1 with 1% mercaptoethanol for 48 hours with continuous agitation (Sage and Gray, 1977). These samples were centrifuged and washed u n t i l the mercaptoethanol odour could not be detected. This was followed by 4 hours of autoclaving (15 lbs., 120 degrees C.) to remove collagen, which i s not s o l u b i l i s e d by guanidine HC1. c. Collagen content. Other samples of aorta were minced, weighed and then soaked in a large volume of d i s t i l l e d water for 24 hours with constant s t i r i n g . This was to remove soluble s a l t s , proteins and carbohydrates. The insoluble material was separated by centrifugation (15 min., 4,300g) and autoclaved in d i s t i l l e d water for 6 hours (15 lbs., 120 degrees C.) to s o l u b i l i s e collagen and pr e c i p i t a t e other proteins. The samples were re-centrifuged (15 min., 14,500g) and the supernatant was put through a 1 um. m i l l i p o r e f i l t e r into a 50 ml volumetric flask. The solution was made up to volume with water. This solution represented the portion of the aorta which was water soluble, not at room temperature, but only with autoclaving. Therefore t h i s should give a crude collagen preparation.The dry weight of the autoclave soluble fraction was then determined by drying aliquots of the solution. The l e v e l of non-collagenous contamination was estimated by comparing the amino acid composition of t h i s f r a c t i o n to published data for 54 octopus collagen. 2. Isolation of E l a s t i c Fibres Samples of e l a s t i c fibres from the internal e l a s t i c a (IE; see chapter I I ) , were prepared in two ways, a) Fresh aortae were cut open, pinned out f l a t on wax, covered with f i l t e r e d sea water and viewed under a dissecting microscope. Pieces of the IE were then stripped from the aorta with fine forceps. These samples are referred to as "native e l a s t i c f i b r e s " , b) Aorta segments were swollen in 98% formic acid for periods of 3 to 6 hours with regular a g i t a t i o n . Formic acid breaks down collagen and muscle proteins (Rasmussen et a l . 1975), and had the eff e c t of loosening the IE so that large pieces could be removed intact.These samples are referred to as "formic acid e l a s t i c f i b r e s " . The IE samples obtained from the above procedures were stored in f i l t e r e d sea water with 1% p e n i c i l l i n + streptomycin at 4 degrees C , and used for mechanical tests of the e l a s t i c material. 3. S o l u b i l i t y of the IE Fibres Native e l a s t i c fibres were tested for s o l u b i l i t y in the following reagents at room temperature (20 to 22 degrees C.) for 12 hours: 1) 4M urea, 2) 6M guanidine HCl with 1% mercaptoethanol, 3) 3M ammonium sulphate, 4) 98% formic acid. IE fibres were also tested by the Lansing method for p u r i f i c a t i o n of e l a s t i n , (Lansing et a l . , 1952) which consists of treatment with 0.1N NaOH at 100 degrees C. for up to an hour, while other samples were subjected to autoclaving 55 in d i s t i l l e d water (15 lbs., 120 degrees C.) for several hours. \ 4. Composition of the E l a s t i c Fibres a. Water content. To determine the water content of the e l a s t i c fibres a c c u r a t e l y ' i t was necessary to keep samples in an equilibrium state of hydration during the weighing procedure. F i r s t , polyethelene "Beem" capsules with snap caps were weighed empty and dry. Native e l a s t i c fibres were is o l a t e d from an aorta and c a r e f u l l y cleaned of any accompanying muscle fragments. Samples of about 300 milligrams were put in open capsules and equilibrated over a solution of 0.08M NaCl in d i s t i l l e d water ( r e l a t i v e humidity = 99.7%) in a vacuum chamber at room temperature. This allowed the fibres to become f u l l y hydrated without any surface condensation. The chamber was opened and the capsules were immediately covered with their caps and then weighed. Next, the capsules were opened and the contents dried over phosphorus pentoxide. Again the the chamber was opened, the capsules covered immediately and weighed. A control capsule showed no change in the water content of the polyethylene throughout this procedure. b. Protein content. Samples of native e l a s t i c f i b r e s were dried, weighed, dissolved in hot a l k a l i (0.1N NaOH, 100 degrees C. for 5 56 min.) and assayed for protein by the method of Dorsey et a l . (1977), using bovine serum albumin and gelatin standards. This i s a heated b i u r e t - f o l i n technique which is equally chromogenic for d i f f e r e n t proteins. c. Carbohydrate content. Native e l a s t i c fibres were also assayed for carbohydrate using the phenol-sulphuric method of Lo et a l . (1970). In this case the samples and standards were heated b r i e f l y (3 min., 100 degrees C.) to dissolve the e l a s t i c f i b r e s . This treatment caused no loss of colour in the standards, and presumably did not affect the determination of carbohydrate in the sample. The assay i s sensitive to any carbohydrate with free or potential reducing groups, and includes hexoses, pentoses and uronic acid but not amino sugars. The results are expressed as glucose equivalents. 5. Amino Acid Analysis Amino acid compositions were determined for the following samples: 1) native e l a s t i c f i b r e s p u r i f i e d with formic acid, 2) formic acid extracts of whole artery wall, 3) guanidine HCl / mercaptoethanol, autoclaved extracts of whole artery wall, 4) autoclave extracted collagen solution. Samples were hydrolysed in 6N HCl at 105 degrees C. for 24 hours in evacuated, sealed tubes. The tubes then broken open and the acid evaporated over phosphorus pentoxide in a vacuum chamber. Some samples were put in sodium c i t r a t e 57 buffer and run through a Beckman 118C automatic amino acid analyser with a 3 hour program, while other samples were run, in lithium c i t r a t e buffer, through the Beckman analyser with a 9 hour program. The short run gave more d i s t i n c t peaks on the chromatogram for cysteine and methionine. The long program gave a more r e l i a b l e determination of hydroxyproline and better separation of threonine - serine, and isoleucine -leucine p a i r s . 6. Force - Extension Tests Fibres isolated from the IE were stretched on a micro-force transducer stage f i t t e d to a Wild M21 po l a r i s i n g microscope (Fig. 3.3). This apparatus has been used previously in the laboratory to study the e l a s t i c properties of single 8 um diameter e l a s t i n fibres (Aaron and Gosline, 1981). It was not possible to i s o l a t e single f i b r e s from the octopus IE because of their small size (less than 5 um). Instead, a bundle of 2 to 5 fibres (around 10 to 15 um t o t a l diameter) was mounted onto the transducer by attaching one end to a slender glass cantilever G, and the other end to a moveable glass plate P, using rubber cement. The two ends of the f i b r e bundle were allowed to a i r dry in order to be glued to the glass, while the middle section of the sample remained in a drop of water. The transducer stage was then flooded with water and covered with a #1 microscope cover-glass. The sample was stretched by s l i d i n g the glass plate P over a thin film of high vacuum grease. The grease kept the 58 Figure 3.3. A) Force-testing platform for e l a s t i c f i b r e s , based on the design on Aaron and Gosline (1981). The sample (S) is glued between the glass cantilever (G) and the plate (P), and i s stretched by s l i d i n g the plate. Force i s calculated from the deflection of G, as measured with respect to the fixed reference, R. Extension in the sample i s measured from the change in separation of surface landmarks on the f i b r e s . 60 plate stationary at each extension. Tensile force in the sample was calculated from the deflection of the cantilever, using simple beam theory: F = 3YId/l^ (3.12) where F i s the t e n s i l e force, d is the l a t e r a l deflection of the cantilever t i p ( r e l a t i v e to a fixed reference), Y i s the Young's modulus for the glass (Y = 6.7 X 10 N/m ), 1 i s the length of the cantilever and I i s the second moment of area which, for a s o l i d cylinder of radius r, i s defined as I = "Tr r^/4. In these experiments 1 was usually about 15mm and r was between 50 and 70 um. Extension of the sample was determined by measuring changes in the spacing of surface features on the f i b r e s . For each sample, the length at which the minimum te n s i l e force was detectable was a r b i t r a r i l y taken as the i n i t i a l unstrained length. A l l measurements were made o p t i c a l l y under the po l a r i s i n g microscope at 300X by using a Wild eyepiece f i l a r micrometer. Based on the r e p r o d u c i b i l i t y of measurements obtained, and a c a l i b r a t i o n of the force transducer with known weights, I estimate the errors in the data reported to be no more than 5%. A l l experiments were done at 20 degrees C. 7. Thermoelastic Tests a. Length - temperature measurements. The thermoelastic experiment requires a correction for the volume changes that occur over the temperature range 61 used. Therefore i t was necessary to assess the swelling behaviour by generating a length - temperature curve for the e l a s t i c f i b r e s . Samples of the IE were impaled on a sharply pointed slender glass filament which was glued to the force transducer stage. A small thermistor probe (1 mm diameter) from an electronic thermometer was placed immediately adjacent to the sample to monitor temperature. The preparation was flooded with water, covered with a #1 coverglass, and viewed under the microscope. A temperature controlled microscope stage was used to heat and cool the preparation. Length measurements were made o p t i c a l l y , with the f i l a r micrometer, over the temperature range 3 to 60 degrees C. b. Force - temperature measurements. If the e l a s t i c f i b r e sample i s held at a fixed length while the temperature i s lowered, the e l a s t i c force may decrease for the following reasons: 1) As the temperature i s lowered the material absorbs water and increases in volume. As a result the fixed length represents a smaller extension r a t i o at the new temperature and the force i s correspondingly reduced. 2) The material i s a rubber and obeys the thermoelastic relationship given by equation (3.6). To test (2) the effects of (1) must be accounted for. A fibre sample mounted on the micro-force transducer was stretched and held at a constant length at 35 degrees C. for two hours. The sample was cooled, in steps of a few degrees, down to 5 degrees C. After two minutes at each temperature the new 62 force was was measured. Then force measurements were made as the sample was heated back to 35 degrees C. 8. Optical Properties During the force - extension tests the presence or absence of o p t i c a l anisotropy ( i . e birefringence) in the e l a s t i c f i bres was determined by observing the specimen between crossed p o l a r i s i n g plates in the microscope. 63 D. RESULTS 1. Composition of the Artery Wall As indicated in Chapter II the major components of the octopus aorta are muscle c e l l s , collagen and e l a s t i c f i b r e s . The water content of the artery wall is 70% by weight. The autoclave soluble f r a c t i o n made up 32% (+/- 2.5%) of the tissue dry weight. The amino acid composition of t h i s f r a c t i o n included 4.2% hydroxyproline and 23.5% glycine. This gives a OHpro/gl.y r a t i o of 0.18. Comparing th i s to a p u r i f i e d octopus skin collagen (Kimura and Matsuura, 1974), which has a OHpro/gly ra t i o of 0.24, i t appears that the autoclave soluble fraction was about 70% collagen. Therefore, the collagen content of the artery wall i s (.70 X 32) = 22.4% of the tissue dry weight. The results of formic acid extractions of pieces of whole artery wall are given in Figure 3.4. This shows that extraction for at least 24 hours is required to remove soluble contaminants, and that longer exposure to formic acid does not reduce the recoverable residue. Now, assuming that the formic acid insoluble f r a c t i o n i s indeed the e l a s t i c f i b r e component, these fibres comprise about 5% of the dry weight of the artery wall. This assumption i s v e r i f i e d below. In addition, the result of a 48 hour extraction of an aorta by the guanidine HCl/mercaptoethanol + autoclave procedure was in agreement with the formic acid data (Fig. 3.4). 64 20 "D CD o CD cr _ 10 JZ CT> CU 5 5 i_ Q i 1 i 1 i 1 1 • 1 1 1 1 r 0 12 24 36 48 60 72 E x t r a c t i o n Time (hr.) Figure 3.4. E l a s t i c f i b r e content of the aorta, determined by formic acid extraction (shaded bars) and by guanidine-HCl/autoclaving (unshaded bars). 65 2. Properties of Isolated E l a s t i c Fibres It was f i r s t noticed that f i b r e s , stripped from the IE of fresh aortae, were highly extensible and e l a s t i c . When stretched, the fibres developed tension and snapped back immediately upon release of the tension. The samples could be stretched repeatedly to large extensions with no apparent damage. However, when allowed to dehydrate the fibres lost their e l a s t i c i t y and became s t i f f and b r i t t l e . Removal of the IE from the aorta was f a c i l i t a t e d by swelling the aorta in formic acid, or by treatment with collagenase. In both cases the IE seemed to loosen as the underlying muscle layer was broken down. This suggests that the fine e l a s t i c fibres which extend from the IE into the artery wall (see F i g . 2.5B) may be linked to the muscle c e l l membranes by some formic acid l a b i l e component. Native e l a s t i c fibres are v i r t u a l l y pure protein. The result of the b i u r e t - f o l i n protein assay was 100% +/-2%. The carbohydrate content was 0.4%. Each gram of native f i b r e s contained 0.53 g. of water. This gives a volume fraction v = 0.40, assuming a value of 1.33 g/cc for the density of dry protein ( i . e . v is the r a t i o of the unswollen protein volume to the water-swollen protein volume). The e l a s t i c f i b r e protein could not be dissolved, and retained i t s e l a s t i c i t y after 12 hours in any of the denaturing agents tested. The protein was also resistant to prolonged autoclaving. These remarkable properties are common only to e l a s t i n . and other protein-rubbers. However, unlike e l a s t i n , the octopus e l a s t i c 66 protein was dissolved within 10 minutes in 0.1N NaOH at 100 degrees C. 3. Amino Acid Analyses Results of the amino acid analyses are given in Table 3.1. Column (f) shows that the e l a s t i c protein from IE samples has a composition d i s t i n c t l y d i f f e r e n t from the protein-rubbers e l a s t i n (g), r e s i l i n (h) and abductin ( i ) . Most noticeable, in the octopus protein, i s the r e l a t i v e l y low glycine content and the presence of many large amino acids. This property i s reflected in the high average residue weight of 110 g/mole. The analysis of the insoluble residue from whole aortae extracted for 6, 18, 24, and 72 hours in formic acid and for 48 hours in guanidine HCl/mercaptoethanol are also given in Table 3.1 (columns a, b, c, d, e). Extraction of aortae for 24 hours or longer gave a constant composition as well as constant weight recovery (see F i g . 3.4), and this composition is v i r t u a l l y i d e n t i c a l to the e l a s t i c protein of the IE. These results support the assumption that the formic acid or guanidine HCl/mercaptoethanol insoluble residue represents only the e l a s t i c protein and that t h i s protein comprises about 5% of the dry weight of the artery wall (Fig. 3.4). The 6 and 18 hour extracts contain a large amount of collagen, as indicated by the high OHproline and glycine content. The collagen contamination contributes to the high weight y i e l d from these extracts (Fig. 3.4). If the e l a s t i c fibres make up 5% of the dry weight of the artery wall, and these fibres 67 Table 3.1 Amino Acid Compositions (residues per thousand). a) to d) formic acid residue of octopus aorta (whole wall) af t e r 6 hr.(a); 18 hr.(b); 24 hr.(c); 72 hr.(d). e) residue of octopus aorta after 48 hr. i n . guanidine hydrochloride and mercaptoethanol. f) formic acid p u r i f i e d internal e l a s t i c a f i b r e s from the octopus aorta. g) e l a s t i n (Sage and Gray, 1977). h) r e s i l i n (Andersen, 1971). i) abductin (Kelly and Rice, 1967). amino acid a b c ASP 85.6 93.9 107.1 THR 41.5 42.4 39.0 SER 56.9 71.1 75.2 GLU 105.5 114.0 125.8 PRO 72.9 67.8 71.9 GLY 212.1 200.3 162.4 ALA 69.4 7917 5318 CYS 2.8 1.0 2.2 VAL 41.1 35.6 38.6 MET 15.9 13.7 7.2 ILE 39.8 38.8 36.1 LEU 59.3 57.2 47.9 TYR 23.3 20.4 20.9 PHE 24.6 20.5 20.5 HIS 10.2 6.9 12.2 LYS 44.3 42.7 28.2 ARG 60.2 65.4 66.2 OH-PRO 40.1 28.8 5 Average residue weight (g/mole) Small amino acids (Gly+Ala+Ser) 100.6 106.7 90.6 6 94 23 59.3 59.3 64.4 15 20 10 81.0 63.0 71.8 12 128 61 132.4 118.0 121.1 19 42 14 41.3 51.3 54.9 113 75 10 88.3 71.6 85.0 313 422 627 74.1 66.8 71.7 244 70 50 10.0 3.7 7.4 — — 1 52.3 65.7 61.9 128 12 5 13.0 21.1 21.0 — — 92 47.3 61.0 59.6 18 9 6 80.7 83.2 73.5 54 30 3 19.2 42.5 36.2 19 12 1 42.3 46.9 42.3 33 12 83 28.4 14.0 21.0 1 12 2 74.7 60.4 68.3 5 8 8 54.9 58.9 45.8 8 46 4 0 5 0 9 — — 110 85 89 79 229 569 620 738 69 contain 53% water (while the whole wall is hydrated to an average of 70%), then the hydrated e l a s t i c f i b r e s w i l l occupy about 3% of the hydrated volume of the artery wall. 4. Force - Extension Tests The long range e l a s t i c properties of the IE f i b r e s were quantified by the force - extension measurements. Fibres mounted in place on the test apparatus could be extended by over 100% without breaking (see F i g . 3.3B,C). At each extension the e l a s t i c fibres reached equilibrium quickly; there was no appreciable hysteresis or change in properties with consectutive cycles of extension. Force - extension data, plotted according to equation 3.2, are shown for native fi b r e s (Fig. 3.5) and for f i b r e s with prior treatment in formic acid (72 hours) followed by rehydration before testing (Fig. 3.6). Recall that a graph of d" ' vs. ( - V7") , for a Gaussian network, yields a straight l i n e with zero intercept and slope = GvY* . Up to)\= 1.5 ( i . e . ^  - V2" = 1.05) the data in both Figs. 3.5 and 3.6 f i t the Gaussian relationship, while at higher extension r a t i o s the points deviate upwards from the straight l i n e . The e l a s t i c modulus G, calculated from the slope of the linear portion of each graph and using v = 0.40, is 4.65 X l0 SN/m^ for the native fibres and 4.62 X 10 N/m for the formic acid f i b r e s . This gives a Young's modulus of 1.4 X 10 N/m for both sets of data. These results indicate that formic acid has no e f f e c t on the e l a s t i c properties of the f i b r e s , at least up to extensions of = 1.5. The data in Figures 3.5 and 3.6 are plotted 70 20r Figure 3.5. Force-extension data for native fibr e samples from the internal e l a s t i c a of the octopus aorta. A linear regression on the data up to (A-X 2 ) = 1.05 had a slope of 3.44 x 10 N/m1 and c o r r e l a t i o n c o e f f i c i e n t , r=0.86. 71 Figure 3.6. Force-extension data for formic acid treated f i b r e s - from the internal e l a s t i c a . A linear regression on the data up to ( A - V 1 ) = 1 .05 had a slope of 3.42 x 10 N/m and a c o r r e l a t i o n c o e f f i c i e n t , r=0.98. 72 together as C T ' V S . ^ in Figure 3.7, along with a polynomial function of best f i t , obtained by least squares regression, for each set of data. Comparison of the two curves confirms that the formic acid fibres are mechanically i d e n t i c a l to native f i b r e s , even in the non-Gaussian range of extensions ( X > 1 . 5 ) . To evaluate the non-Gaussian parameter s (the number of random lin k s between c r o s s - l i n k s ) , the experimental curve for native fibres is compared to plots of equation 3.5 for d i f f e r e n t values of s (Fig. 3.8). Although the curve for the e l a s t i c f i b r e s does not have the exact shape of any one the o r e t i c a l curve i t does f a l l between the plots of s = 4 and s = 5 at extensions greater than 1.6. On the basis of t h i s analysis i t i s concluded that there are, on average, 4 or 5 functional random lin k s between cross- l i n k s in the molecular network of the octopus elastic* protein. 5. Optical Properties The s t r e s s - o p t i c a l properties of the e l a s t i c f i b r e protein were assessed q u a l i t a t i v e l y in this study. It was noted that a l l specimens became highly birefringent when stretched, but were non-birefringent when relaxed (see F i g . 3.9). The significance of t h i s observation i s that i t supports the hypothesis that, l i k e a rubber, the octopus e l a s t i c protein i s an amorphous random-coil molecular network which i s mechanically and o p t i c a l l y isotropic when unstrained. Deformation of a rubber disturbs the network, 73 20r 1.0 1.2 U 1.6 1.8 2.0 2.2 Ex tens ion Ratio X Figure 3.7. Force-extension data from Figures 3.5 and 3.6 plotted as CT' vs. X , along with the best f i t polynomial functions. Open c i r c l e s and broken l i n e are data from formic acid treated f i b r e s ; closed c i r c l e s and s o l i d l i n e are data from native f i b r e s . 74 1.0 1.2 U 1.6 1.8 2.0 2.2 E x t e n s i o n Ratio X Figure 3.8. Non-Gaussian properties of the IE f i b r e s . The polynomial force-extension curve for the native f i b r e s , shown in Figure 3.7, i s compared to plots of equation 3.5 for d i f f e r e n t values of s. The ordinate i s normalised to the force per chain by dividing the stress by the modulus. 75 Figure 3.9. A) A sample of unstretched e l a s t i c fibres seen under polarized l i g h t . The fi b r e s are not birefringent here. B) The same as (A) but with the sample stretched by 100 per cent. Now the e l a s t i c f i b r e s are highly b i r e f r i n g e n t . 77 making i t physically anisotropic, that i s , the chains are forced to take some degree of orientation toward the d i r e c t i o n of the applied load. This results in a strain induced birefringence which should increase as a linear function of deformation (Treloar, 1975). Birefringence in the octopus e l a s t i c fibres increased with the degree of extension, but the actual stress-birefringence relationship was not studied q u a n t i t a t i v e l y . 6. Thermoelasticity The effect of temperature on the swollen dimensions of, e l a s t i c fibres is shown in F i g . 3.10. The data have been normalised by expressing specimen length as a proportion of the length at 20 degrees C, the temperature at which the volume f r a c t i o n , v, was determined. The length of the fibre sample i s a linear function of temperature from 0 to 35 degrees C, with a c o e f f i c i e n t of linear expanison of -.001 (change in length per degree). Therefore the thermoelastic measurements were made over this temperature range. Above 35 degrees C. there appears to be a sharp decrease in sample length. A collagen- l i k e contaminant, melting at this temperature, might cause the fibres to shorten; however the amino acid composition data in Table 3.1 c l e a r l y indicate an absence of collagen from the IE f i b r e s . The explanation of thi s observed s h i f t in the swelling curve at 35 degrees C. remains uncertain. Figure 3.11 demonstrates that the force required to 78 0 10 20 30 ^0 * ° Temperature ( ° C ) Figure 3.10. The effect of temperature on the swollen length of unstretched e l a s t i c f i b r e s . 79 5 a ______ - ^ J ^ 1 ^ -_r-_r-T- - - - ""a A rsi z L O O 1 . 4 2 • b Force 1 . 2 2 1 1 1 1 i i i 0 1 0 2 0 3 0 AO Temperature ( °C) Figure 3.11. Force-temperature p l o t s . Force was measured in e l a s t i c f i b r e s held at constant length while the temperature was varied. Linear regression l i n e s ( s o l i d lines) for experiments at lengths of 1.62 (a), 1.42 (b), 1.22 (c) ar b i t r a r y units are drawn through the data points. The unstrained length at 20 degrees C was defined as 1.0 units. Regression lines for data after correction to constant extension r a t i o are also shown (broken l i n e s ) . 80 hold a fi b r e sample at constant length increases l i n e a r l y with temperature, and that the slopes of the force length plots (a,b,c) increase with length (here the force is given as Newtons / meter % (N/m2) of unstrained swollen cross-sectional area at 20 degrees C.) In addition, Figure 3.11 shows regression l i n e s for the data when corrected from constant length to constant extension r a t i o (a',b',c'). Recall that A for a fi b r e which i s held at constant length w i l l increase as temperature increases due to decreased swelling (Fig. 3.10). To obtain the corrected force-temperature curves the following procedure was used: Force-length isotherms (Fig. 3.12) were plotted d i r e c t l y from the uncorrected data in F i g . 3.11 (the length scale has arb i t r a r y units such that the unstrained length at 20 degrees C. i s equal to 1.0). The zero-force lengths of the other isotherms were taken from the free swelling data (Fig. 3.10). Based on these starting dimensions, lines of constant A were then plotted across the isotherms (diagonal l i n e s , F i g . 3.12). Now the force-temperature curves for constant A can be drawn and these are shown in F i g . 3.11. In p r i n c i p l e the swelling correction reduces the slope of the force-temperature curves by eliminating the increase in force with temperature that arises due to the decrease in swelling. The l i n e a r i t y of the force-temperature curves allows us to proceed with the thermodynamic analysis of the constant length data according to eqn. 3.8, and of the constant A data according to eqn. 3.11. The results are given in Table 3.2 and plotted in Figure 3.13 for T = 20 degrees C. When 81 uncorrected for volume changes, extension of the e l a s t i c fibres appears to be associated with a large negative enthalpy change, (dH/dL)T,P, and concomitantly a large decrease in entropy, -T(dS/dL)T,P. However, when the same data are analysed in terms of constant )\ (swelling correction) the internal energy change ,(dU/dL)T,V, i s much less than the enthalpy change. In fact (dU/dL)T,V i s close to zero at low extensions, as predicted by the kinetic theory for an ideal rubber. The slope of the corrected force-temperature curves represents the decrease in entropy, (dS /dX)T,V, that results from deformation of the molecular network at constant volume. This change in entropy accounts for almost a l l of the e l a s t i c force at extensions up to A = 1.42, and for 77 % of the force at A= 1.62 (Table 3.2). 82 Figure 3.12. A plot of force-length isotherms derived from the data in Figure 3.11. For temperatures of 5, 10, 15, 20, 25, .30 and 35 degrees C, force values were taken from the regression l i n e s a, b, and c in Figure 3.11, and plotted as a function of length in Figure 3.12. Based on the swelling data for the e l a s t i c f i b r e s (Fig. 3.10), l i n e s of constant extension r a t i o were drawn across the isotherms. Force-extension data were then taken from the points of intersection of the isotherms and the l i n e s of constant extension r a t i o , and replotted as regression lines in Figure 3.11. Table 3.2 Thermoelastic data at 20°C for three d i f f e r e n t specimen lengths Extension Force (105N/m2) Enthalpy Entropy Enthalpy Energy Entropy Energy (L or X) (3H/9L) T / P - T O S / 3 L ) T f P Force (9U/8X ) T ^ V -TOS/3X ) T y Force 1.22 1.34 -3.47 4.81 -2.59 -0.12 1.46 -0.09 1.42 2.69 -3.02 5.71 -1.12 0.12 2.57 0.05 1.62 4.49 -2.84 7. 33 -0.63 1.02 3.47 0.23 85 Figure 3.13. Force-length curve for the e l a s t i c f ibres at 20 degrees C , resolved into the corresponding entropy and enthalpy components according to eqn. 3.6 (broken l i n e s ) . The changes in entropy and internal energy for deformation at constant extension r a t i o , calculated according to eqn. 3.9, are also plotted ( s o l i d l i n e s ) . S=entropy, U=internal energy, H=enthalpy. 86 E. DISCUSSION 1 . Network Properties This study presents several l i n e s of evidence to support the hypothesis that presumptive e l a s t i c fibres found in the wall of the octopus aorta are composed of highly extensible rubber-like protein molecules. Like previously described protein rubbers,- t h i s cephalopod protein (which w i l l be c a l l e d octopus a r t e r i a l elastomer - OAE) appears to have the necessary physical and chemical properties to conform to the kinetic theory of rubber e l a s t i c i t y . Like most e l a s t i c polymers and l i g h t l y crosslinked rubbers the OAE fibres have a r e l a t i v e l y low modulus of e l a s t i c i t y (G = 4.7 X 10 N/m , and large e x t e n s i b i l i t y (>100%). These properties, along with the high degree of i n s o l u b i l i t y are consistent with the model of a crosslinked network of thermally agitated, f l e x i b l e , random molecules. The network is hydrated under physiological conditions, with the volume fraction of protein in a swollen sample, v = 0.40 at 20 deg.C. For e l a s t i n , which is more hydrophobic, v = 0.55 at 20 degrees C. (Gosline, 1978b). R e s i l i n and abductin are also water swollen in vivo, with v equal to about 0.45 and 0.5 respectively (Weis-Fogh, 1961b; Alexander,1966). Like other protein-rubbers the OAE fibres become b r i t t l e and glassy when dehydrated. To have rubber-like properties the network chains must be k i n e t i c a l l y free and have a random configuration. Without water (or some other polar solvent) protein chains w i l l f o l d into a fixed conformation, held by intra-chain 87 hydrogen bonds. Presumably water disrupts these hydrogen bonds and imparts kinetic freedom to the network (Gosline, 1976, 1978a). Random conformation in the OAE molecular network i s implied by the observation that the f i b r e s , l i k e e l a s t i n and r e s i l i n , are non-birefringent when unstressed in contrast to the large i n t r i n s i c birefringence of highly ordered protein molecules such as collagen f i b r e s . When stretched to large extensions the OAE fibres become highly birefringent, as do other protein rubbers, presumably because deformation imposes a preferred orientation upon the network chains, and t h i s gives r i s e to o p t i c a l anisotropy. The intensity of birefringence increases with the degree of extension, but t h i s awaits a more detailed study to determine the exact stress-birefringence r e l a t i o n in t h i s protein. Optical properties have been studied q u a n t i t a t i v e l y in r e s i l i n (Weis-Fogh, 1961b) and e l a s t i n (Aaron and Gosline, 1980), and found to be in agreement with the predictions of the kinetic theory. That the molecules of the OAE protein are held together by stable covalent crosslinks i s shown by the long-range reversible e l a s t i c properties ( i . e . , there was v i r t u a l l y no "creep" in extended samples) and by the high degree of i n s o l u b i l i t y of the f i b r e s in protein solvents such as formic acid. The observation that the OAE was not denatured in these solvents is suggestive that the protein chains are e s s e n t i a l l y denatured in the native state; that i s , they are k i n e t i c a l l y free, random c o i l molecules. 88 Having determined the e l a s t i c modulus, i t is possible to estimate the average molecular weight of the chains between crosslinks, using equation 3.3. For the OAE protein Mc i s 6,900 grams/mole. In theory, th i s equation relates to a network in which four chains meet at each junction point (Treloar, 1975). Imperfections such as loose ends w i l l contribute to an overestimate of Mc. A correction to eqn. 3.3 has been developed (Treloar, 1975): G = £>RT/Mc (1-2Mc/M) (3.13) where M i s the molecular weight of the uncrosslinked precursor molecule. Nothing i s known about the precursor of the OAE protein, but based on evidence for e l a s t i n and r e s i l i n (Sandberg, 1976; Weis-Fogh, 1961b) i t is reasonable, as a f i r s t approximation, to estimate M at about 10^ grams/mole. The "corrected" value of Mc from eqn. 3.13 would be 6100 grams/mole. We may expect, therefore, that the molecular weight between crosslinks in OAE i s approximately 6100 to 6900 grams/mole. Since the average amino acid residue weight for the protein i s 110 grams/mole, t h i s means that each chain w i l l be about 55 to 63 amino acids long. Now, from the non-Gaussian analysis (Fig. 3.8), i t was estimated that about 5 random links make up each chain. It appears, therefore, that 12 to 14 amino acids are necessary to give one "functional " random l i n k , and since each amino acid provides two single bonds of rotation, the random link in the octopus protein requires about 25 rotational bonds. This suggests that the f l e x i b i l i t y of the network is f a i r l y 89 r e s t r i c t e d , but does not imply that the conformation i s non-random. Rather, ideal deformation of the network is limited to small extensions, i . e . the Gaussian behaviour is seen only at r e l a t i v e l y low A . This network property undoubtedly arises from the high proportion of amino acids with large side groups (eg. phenylalanine, tyrosine, aspartic acid, glutamic acid) which cause s t e r i c hindrances in bond rotation (Dickerson and Geis, 1969). In contrast to OAE, natural polyisoprene rubber, with.Mc = 8310 grams/mole has s 75 and each random link corresponds to only 1.6 isoprene residues, or 4.8 rotational bonds (Treloar, 1975). Other protein-rubber networks are also much less f l e x i b l e than isoprene rubber, but s l i g h t l y more f l e x i b l e than the OAE molecule. This c h a r a c t e r i s t i c i s reflected in the value of s and the average residue weight. For e l a s t i n s i s about 10 and the average amino acid residue is 85 grams/mole (Aaron and Gosline, 1981), for r e s i l i n s i s about 7 and the average amino acid residue weight i s 89 grams/mole (Weis-Fogh, 1961b). This gives the number of amino acids per random link as 7 to 8 for e l a s t i n and 8 to 9 for r e s i l i n . The somewhat more f l e x i b l e e l a s t i n molecule becomes non-Gaussian at s l i g h t l y higher extensions than the other two proteins (Fig. 3.14). 2. Thermoelastic Properties The thermodynamic analysis of the OAE protein, tested in water as an open system, shows that the e l a s t i c force has a large negative enthalpy component (Fig. 3.13). In fact, at 90 Figure 3.14. Force-extension curves for rubber-like proteins ( s o l i d lines) compared to the theoret i c a l Gaussian curve for a rubber (broken l i n e ) . The ordinate is normalised to the force per chain by di v i d i n g stress by the modulus for each material. 91 low extensions the enthalpy change i s more than twice as great as the t o t a l force (Table 3.2). Consequently, the decrease in entropy i s also much larger than the force, "in order to s a t i s f y equation 3.6. A similar result was obtained for hydrated e l a s t i n tested as an open system (Meyer and F e r r i , 1936). This result was o r i g i n a l l y attributed i n c o r r e c t l y to strain-induced c r y s t a l l i s a t i o n , which does occur in natural rubber at very high extensions (Fig. 3.2B). It i s now known that the very large enthalpy change i s a d i r e c t result of swelling changes that occur in the e l a s t i n molecule. S p e c i f i c a l l y , t h i s involves changes in enthalpy associated with mixing of water and non-polar side groups in the protein (Gosline, 1976). It appears that the large negative enthalpy term observed for the OAE f i b r e s in t h i s study may also be attributed to changes in temperature dependent network swelling. When the data are corrected to constant extension r a t i o , the internal energy change is reduced to nearly zero and the e l a s t i c force is predominantly due to changes in the conformational entropy of the system, in accordance with the kinetic theory (Fig. 3.13; Table 3.2). However, (dU/dX)T,V at X = 1.62 i s not t r u l y zero, but actually represents 23% of the t o t a l force, and this warrants further discussion. At high extensions there may be, in fact, a small positive internal energy contribution to the e l a s t i c force due to interactions between chains. On the other hand, (dU/dX)T,V may be e s s e n t i a l l y zero, and the result for X = 1.62 may 92 represent an over-correction of the data. The temperature swelling relationship for the e l a s t i c f i bres has been studied only for samples under no t e n s i l e load (Fig. 3.10). The degree of swelling of a polymeric molecule i s inversely proportional to the network s t i f f n e s s (Flory, 1953). Since the OAE protein i s in the non-Gaussian region at X = 1.62 (Fig. 3.8), the network s t i f f n e s s has e f f e c t i v e l y increased, and therefore one might expect the magnitude of the swelling change with temperature to be l e s s . The swelling correction that was applied is probably quite v a l i d for extensions in the Gaussian region but may be too large at extensions where the network becomes s t i f f e r and non-Gaussian; thus (dU/d).)T,V may have been overestimated at the high extension. 3. The Role of the E l a s t i c Fibres in the Octopus Aorta Although there are several h i s t o l o g i c a l reports on the widespread occurrence of " e l a s t i c f i b r e s " in the invertebrates (see Elder, 1973), the present study is unique in providing the f i r s t instance where presumptive e l a s t i c f ibres have been isolated from an invertebrate's blood vessel, analysed chemically and tested mechanically. The results support the hypothesis proposed in Chapter II, that i s , the connective tissue f i b r e s which form the internal e l a s t i c a of the octopus aorta and the extensions of the IE into the artery wall are indeed rubber-like. Further, t h i s mechanical evidence validates the results of the aldehyde fuchsin technique for i d e n t i f y i n g e l a s t i c f i b r e s , and thus gives credence to other claims of e l a s t i c fibres in 93 invertebrate tissues for which there is h i s t o l o g i c a l evidence only. The octopus e l a s t i c fibres have the necessary mechanical properties to provide e l a s t i c i t y in the artery wall, in a way that i s analogous to the role of e l a s t i n in the verterbates. This hypothesis w i l l be investigated in the next chapter. The i s o l a t i o n and characterisation of the OAE in t h i s study adds a s i g n i f i c a n t contribution to our f a i r l y limited knowledge of a unique class of molecules, the protein-rubbers. The tremendous variation in amino acid composition among the four known protein-rubbers (Table 3.1) suggests that each protein arose independently during evolution in response to selection for similar mechanical design. The intriguing question of what type of sequence patterns allow these special proteins to exist as random, k i n e t i c a l l y free chains i s s t i l l very much an open question (Gosline, 1980). In contrast, other proteins have stable conformations which arise uniquely from each amino acid sequence. Based on the compositions of e l a s t i n , r e s i l i n and abductin i t has been suggested that a large proportion of the small amino acids (glycine, alanine and serine) may be necessary in order to minimise s t e r i c hindrances and permit a k i n e t i c a l l y free network to exist under normal physiological conditions. Table 3.1 shows that this prediction does not hold for the OAE protein, where glycine, alanine and serine together make up only 23% of the composition, compared to 55 to 74% in the other protein-rubbers. 94 An alternative strategy in "designing" a- protein-rubber might be to have a high proportion of charged amino acids (asp, glu, arg, lys) which may prevent the formation of stable secondary structures. The charged amino acids account for 33% of the OAE protein. Of course the large side groups on the charged amino acids may hinder the f l e x i b i l i t y of the molecular chains, as discussed above. However, a r e l a t i v e l y i n f l e x i b l e network which becomes non-Gaussian at low extensions is probably a desireable c h a r a c t e r i s t i c for a protein-rubber (such as the OAE protein) which i s required to provide e l a s t i c reinforcement in the wall of a blood vessel. The reasons for t h i s w i l l be discussed later in conjunction with the results of tests on the mechanical properties of the intact octopus aorta. 95 CHAPTER IV. MECHANICAL PROPERTIES OF THE OCTOPUS AORTA A. INTRODUCTION Studies on the mechanical properties of vertebrate blood vessels have been numerous over the l a s t century, since the pioneering work of C.S. Roy (1880). He gave a detailed quantitative description of the long-range e l a s t i c behaviour of mammalian a r t e r i e s , which showed that these vessels are highly d i s t e n s i b l e at physiological pressure and have thermodynamic properties which are similar to those of natural rubber. More recent studies have continued to expand on these fundamental observations (recent reviews include McDonald, 1974; Dobrin, 1978; Cox, 1979; Bauer et a l . , 1982). We now know that the mammalian artery wall has non-linear e l a s t i c properties which ari s e from a complex arrangement of two connective tissue elements: a rubber-like protein, e l a s t i n , and a s t i f f fibrous protein, collagen. At low pressures in the physiological range the artery wall is highly compliant, as the pressure is resisted largely by the e l a s t i n . With increasing pressures in the physiological range and above, the artery wall becomes much less extensible due to the recruitment of more e l a s t i n fibres and also to the transfer of load to the collagen network. The role of the a r t e r i e s as a passive, e l a s t i c component in the high pressure closed c i r c u l a t o r y system of mammals has long been appreciated (see MacDonald, 1974). In addition to being blood conduits, large a r t e r i e s are important in 96 reducing the p u l s a t i l i t y of blood flow from the heart to the body tissues. The ar t e r i e s are distended with blood during systole, while passive e l a s t i c r e c o i l provides continued flow during d i a s t o l e . In l i g h t of thi s behaviour the e l a s t i c a r t e r i a l tree has been represented by a capacitance element in mechanical and e l e c t r i c a l analogues of c i r c u l a t i o n (see Noordergraaf, 1969). It i s well established that the e l a s t i c properties of the large a r t e r i e s are an important determinant of the dynamics of blood flow in the cardiovascular systems of mammals (McDonald, 1974) as well as other vertebrates (Speckman and Ringer, 1966; Satchell, 1971; Lan g i l l e and Jones, 1975, 1977; Burggren, 1977). Apparently, there are no reports in the l i t e r a t u r e on the mechanical properties of blood vessels from any invertebrate animal. This i s not surprising since most invertebrates have r e l a t i v e l y simple, low pressure, open c i r c u l a t o r y systems (Martin and Johansen, 1966). Cephalopods, however, are one group in which the c i r c u l a t i o n of blood has attained a high l e v e l of complexity; the c i r c u l a t o r y system of cephalopods i s closed, and has a well developed network of blood vessels (Wells, 1978; Browning, 1980). Observations on the blood pressures in octopus (Johansen and Martin 1962; Wells 1979), nautilus (Bourne et a l . 1978) and squid (Bourne, 1982) suggest that the large a r t e r i e s function as an e l a s t i c reservoir in these animals. In the preceeding chapters, i t was shown that the octopus aorta has a connective tissue network which is made 97 up of a protein with rubber-like properties, the octopus a r t e r i a l elastomer, OAE. It was proposed that this protein was the functional analogue of e l a s t i n , and that the octopus aorta might have long-range e l a s t i c properties based on th i s material. In the following study th i s hypothesis i s tested experimentally by a quantitative analysis of the mechanical properties of the octopus aorta. The experiments described below demonstrate that the octopus aorta exhibits non-linear, v i s c o e l a s t i c properties which resemble those of vertebrate a r t e r i e s . That is to say, the mechanical response of the artery wall has both instantaneous ( e l a s t i c ) and time dependent (viscous) components, and the modulus of e l a s t i c i t y ( i . e . the s t i f f n e s s ) increases continuously with the degree of s t r a i n . These results show that the octopus aorta i s suitably designed to function as an e f f i c i e n t e l a s t i c energy storage element in the c i r c u l a t o r y system, and that the e l a s t i c properties of the artery wall, in the physiological range of pressures, can be attributed to the presence of the rubber-like protein f i b r e s which we have c a l l e d the OAE. 98 •B. ANALYTICAL METHODS 1. Linear E l a s t i c i t y Hookes Law states that when a t e n s i l e force is applied to an "ideal e l a s t i c s o l i d " the resulting deformation w i l l be d i r e c t l y proportional to that force. A Hookean material i s characterised by the Young's modulus of e l a s t i c i t y (Y), a measure of the s t i f f n e s s . Y i s defined as the r a t i o of stress (cr) to s t r a i n (e): Y = ff/€ (4.1) Stress i s calculated as the force (F) divided by the cross-sectional area (A) over which the force i s applied 0" = F/A (4.2) Stress has units of Newtons/meter (n/m ). Strain i s a dimensionless quantity which defines the deformation as a r e l a t i v e change in length €= (L-Lo)/Lo = AL/Lo (4.3) where L is the stressed sample length, and Lo is the i n i t i a l , unstressed length. Thus for a Hookean s o l i d the s t r e s s - s t r a i n curve i s linear and Y i s a constant (Fig. 4.1A). For small s t r a i n s , eqn. 4.1 describes the e l a s t i c behaviour of materials which are very s t i f f and r e l a t i v e l y inextensible 1° it such as glass or steel (for which Y = 7 X 10 and 2 X 1 0 N/m respectively). 99 F i g u r e 4.1. S t r e s s - s t r a i n s curves f o r a l i n e a r m a t e r i a l (A) and a n o n - l i n e a r m a t e r i a l (B). In (A) the Young's modulus i s equal to s t r e s s / s t r a i n and i s the same f o r a l l l e v e l s of s t r a i n . In (B) the T a n g e n t i a l modulus i s taken as the slope of the s t r e s s - s t r a i n curve and v a r i e s with the l e v e l of s t r a i n (point 1. vs. p o i n t 2 ) . 100 2. Nonlinear E l a s t i c i t y in Thick-walled Tubes The important differences between l i n e a r l y e l a s t i c Hookean so l i d s and rubber-like polymers have been discussed in the previous chapter. In general, soft b i o l o g i c a l tissues l i k e artery wall are highly extensible and do not show linear s t r e s s - s t r a i n relationships. Therefore the e l a s t i c modulus i s not constant, but rather i t i s strain-dependent. For such non-Hookean materials i t is inappropriate to use Young's modulus to characterise the s t i f f n e s s . Instead, the tangential modulus of e l a s t i c i t y (E) is defined, for a given l e v e l of s t r a i n , as the slope of the s t r e s s - s t r a i n curve at that s t r a i n (see F i g . 4.1B) E = A 0 - / A C (4.4) This equation applies only to s t r e s s - s t r a i n data obtained from the extension (or compression) of a material in a single d i r e c t i o n by a l i n e a r l y applied force. The mechanical properties of a r t e r i e s can be measured in v i t r o by uniaxial tests on s t r i p s and rings, and in these cases Eqn. 4.4 i s v a l i d . However, i t is much more desireable to use i n f l a t i o n tests on intact vessel segments so as to more close l y mimic the in vivo s i t u a t i o n (Bergel, 1961a; Dobrin, 1978). A thick-walled e l a s t i c tube at equilibrium with a distending pressure (P) w i l l experience t e n s i l e forces in two perpendicular directions simultaneously, i . e . circumferential and longitudinal (Fig. 4.2A). There w i l l also be a 101 F i g u r e 4.2. A) Diagram of an a r t e r i a l segment to show the c i r c u m f e r e n t i a l (C) and l o n g i t u d i n a l (L) d i r e c t i o n s . R i s the ouside r a d i u s , r i s the i n s i d e r a d i u s , and h i s the w a l l t h i c k n e s s . B) Diagram to i l l u s t r a t e Poisson's r a t i o s . A u n i a x i a l l y a p p l i e d f o r c e (F) i n the l o n g i t u d i n a l d i r e c t i o n causes narrowing i n the c i r c u m f e r e n t i a l and r a d i a l d i r e c t i o n s ( l e f t diagram). A u n i a x i a l f o r c e i n the c i r c u m f e r e n t i a l d i r e c t i o n causes a r e d u c t i o n i n the l e n g t h and a narrowing i n the r a d i a l d i r e c t i o n ( r i g h t diagram). P r e s s u r i s e d a r t e r i e s are s u b j e c t e d to both l o n g i t u d i n a l and c i r c u m f e r e n t i a l f o r c e s . 1 02 compressive force acting r a d i a l l y , but since t h i s w i l l be r e l a t i v e l y small (Dobrin, 1978) i t is ignored here in order to simplify the analysis. The circumferential stress in the wall (CTc) is given by 0~c = Pr/h (4.5) where r i s the inside radius and h is the wall thickness. Strain in the circumferential d i r e c t i o n i s calculated at the mid-wall radius as C c = AR / Ro (4.6) where R = (R + r)/2, R i s the outside radius and Ro i s the unstressed mid-wall radius. Stress in the longitudinal d i r e c t i o n (0~"l) is given by CTl = p r a/2 R h (4.7) As R/h increases, R approaches r and 0" 1 approaches (Tc/2. Longitudinal s t r a i n (€"1) is given as € 1 = AL/Lo (4.8) where Lo i s the unstressed vessel segment length. When an artery i s pressurised i t is loaded b i a x i a l l y , and the relationship between stress, strain and moduli become more complex than the one given by eqn. 4.4. For example, a s t r a i n increment in the circumferential d i r e c t i o n w i l l be dependent on the stress increment and the e l a s t i c modulus in that d i r e c t i o n , but i t w i l l also be influenced by the s t r a i n 103 increment which occurs simultaneously in the longitudinal d i r e c t i o n . The interaction between pairs of perpendicular strains in a material i s described by a parameter c a l l e d Poisson's r a t i o (v*). Consider the wall of an e l a s t i c tube (Fig. 4.2); i f the material i s incompressible, then extension in one direction by a uniaxial force i s accompanied by a decrease in the two l a t e r a l dimensions. For a mechanically anisotropic tube ( i . e . the longitudinal modulus E l i s not equal to the circumferential modulus Ec) such as an artery, at least two Poisson's ra t i o s are necessary to describe the relati o n s h i p between C c and Cl. These are i d e n t i f i e d as V c l = - A £ c / A&1 (4.9) and -Vic = - &£1/A£C (4.10) where V c l i s the r a t i o of circumferential to longitudinal strains when the structure i s subjected to a longitudinal stress only (Fig. 4.2 ) and V i c i s the r a t i o of longitudinal to circumferential A when the structure i s subjected to a circumferential stress only (Fig. 4.2 ). Values of V usually vary between 0 and 1.0. The Poisson's ratios are dependent on the e l a s t i c moduli as follows: V l c / E c = V c l / E l (4.11) When an artery is i n f l a t e d the increase in circumference w i l l tend to cause a decrease in length-, while the action of the pressure w i l l be to lengthen the vessel. Whether the artery actually lengthens or shortens, and by how much, i s dependent on the Poisson's ratios and the r e l a t i v e 104 values of the e l a s t i c moduli. Dobrin and Doyle (1970) provide a method for estimating these parameters from i n f l a t i o n t e s ts. The following equations describe the simultaneous st r a i n increments for a given pressure increment (Dobrin and Doyle, 1970; Patel and Vaishnav, 1977) Adc = ( A^c/Ec) -V c l ( A ^ T l / E l ) (4.12) Atl = ( 4 < T i / E l ) - 1 / c l ( 4<Tc/El) (4.13) It can be seen by comparison with eqn. 4.4 that the b i a x i a l strains w i l l be less than uniaxial strains by an amount which is dependent on V . Clearly, then, the slope of the b i a x i a l s t r e s s - s t r a i n curve i s not a dir e c t measure of E. The analysis using equations 4.12 and 4.13 i s based on the assumptions that 1) r a d i a l stresses are small enough to ignore, 2) shearing stresses do not occur, and 3) the artery wall i s incompressible. The f i r s t two assumptions greatly simplify the mathematics involved. The incompressibility assumption is useful because i f the volume of a vessel segment is known, then measurement of two of i t s dimensions allows c a l c u l a t i o n of the t h i r d dimension (The inside radius, r, i s usually calculated from measurements of the outside radius, R, and the length, L ) . Stresses and strains are determined from i n f l a t i o n data using equations 4.5 to 4.8. This leaves Ec, E l and V c l as unknowns. Dobrin and Doyle (1970) determined E l from uniaxial extensions and then solved equations 4.12 and 4.13 simultaneously for V c l and Ec. The same procedure is followed in the experiments reported here. 105 3. V i s c o e l a s t i c Behaviour The analysis presented so far considers that the artery wall is an e l a s t i c structure for which the mechanical response i s independent of time, and that true equilibrium values of stress, s t r a i n and modulus can be determined for each pressure increment. In r e a l i t y , b i o l o g i c a l materials exhibit time and frequency dependent e l a s t i c i t y because they have the properties of both e l a s t i c s o l i d s and viscous f l u i d s . A perfectly e l a s t i c s o l i d deforms instantly, under a given stress, to a s t r a i n which then remains constant with time. Removal of the stress allows the instantaneous recovery of the o r i g i n a l dimensions because a l l the work done in deformation i s stored as e l a s t i c energy and can be recovered without loss (Wainwright et a l . , 1976). On the other hand, a stress applied to a purely viscous f l u i d w i l l cause continuous flow at a rate which is determined by the v i s c o s i t y . In general, stress increases with deformation rate. Energy used to drive viscous flow i s lost as heat and is not recovered e l a s t i c a l l y . The response of a v i s c o e l a s t i c material to stress or s t r a i n w i l l f a l l somewhere between these two extremes and w i l l depend on the r e l a t i v e contribution of the e l a s t i c and viscous components. V i s c o e l a s t i c i t y can be characterised in several ways. One r e l a t i v e l y simple technique is to measure the decay of stress, with time, in a sample after rapid deformation to a fixed s t r a i n . This phenomenon is c a l l e d stress-relaxation. Another technique involves the c y c l i c loading of a specimen 106 at constant str a i n rate. The energy lost per cycle, expressed as a percentage of the t o t a l energy input, i s known as the hysteresis. This can be calculated d i r e c t l y from the areas under the load and unload portions of the s t r e s s - s t r a i n or pressure-volume curves. Hysteresis i s a direct measure of the viscous contribution to the mechanical properties of the material. Perhaps the most appropriate method of quantifying the v i s c o e l a s t i c properties of a r t e r i e s involves dynamic testing over a range of frequencies. This technique provides a direct measure of the v i s c o e l a s t i c i t y at each frequency in a form that can readily be applied to the analysis of a r t e r i a l hemodynamics. In dynamic tests a sinusoidally varying str a i n is imposed on a sample, and the resulting stress o s c i l l a t i o n s are observed at each frequency. If the material exhibits linear v i s c o e l a s t i c i t y then the stress w i l l vary sinusoidally and w i l l be phase shifted ahead of the st r a i n o s c i l l a t i o n by an angle, <5 . The magnitude of <S indicates the r e l a t i v e importance of v i s c o s i t y to the o v e r a l l mechanical response of the material. In theory, & may vary from 0 degrees for pure e l a s t i c i t y to 90 degrees for pure v i s c o s i t y . The r a t i o of stress amplitude (ACT) to s t r a i n amplitude (A-e ) gives the dynamic e l a s t i c modulus (E*) for each frequency (by analogy to equation 4.4). E* is a complex quantity and can be resolved into two components as follows (Ferry, 1970): E', the storage modulus, is derived from the component of stress which i s in phase with str a i n and is proportional to the e l a s t i c energy stored 1 07 in each cycle. E' ' , the loss modulus, represents the out-of-phase component of stress and i s proportional to the viscous energy loss per cycle. E' and E'' are determined from measured values of E* and 6 by these equations: E' = E* (cos S ) (4.14) E " = E* (sin 6 ) (4.15) The r a t i o E''/E' is equal to tangent cS , and this i s c a l l e d the damping term. Tan 6 i s useful as an indication of the r e l a t i v e viscous energy loss per cycle, which can be related to hysteresis. E'' can be used to calculate the dynamic v i s c o s i t y n', from the angular frequency w by (Hardung, 1953): E''=n'w (4.16) The dynamic v i s c o s i t y i s most useful in describing the behaviour of un-crosslinked polymers, i . e . , v i s c o e l a s t i c f l u i d s . In a complex structure l i k e an artery wall, the physical interpretation of n' i s very d i f f i c u l t , but i t has been included here since i t i s referred to in most studies of dynamic properties of a r t e r i e s . The preceding analysis i s based on a linear v i s c o e l a s t i c model which consists of one e l a s t i c element and one viscous element arranged in p a r a l l e l (Voigt Model). Such a simple model does not adequately represent the non-linear v i s c o e l a s t i c behaviour of blood vessels over large deformations (Cox, 1972; Gow, 1972). However, i f the s t r a i n 108 amplitude i s s u f f i c i e n t l y small, so that the stress response is e s s e n t i a l l y linear, then equations 4.14 and 4.15 provide a useful way to separate and quantify the e l a s t i c (E') and viscous (E 1') components for a single frequency (Fung, 1981). 4. Dynamic Incremental E l a s t i c i t y A r t e r i e s in vivo are subjected to two simultaneous stresses, a st a t i c one a r i s i n g from the mean blood pressure and a dynamic one which results from the pressure pulse of each cardiac cycle. To simulate these conditions in v i t r o , the dynamic test adds small sinusoidal stress o s c i l l a t i o n s to a s t a t i c a l l y imposed load. Measurements of the dynamic properties of arteries are useful for predicting hemodynamic parameters such as pulse wave ve l o c i t y (see chapter V). It seems most appropriate to describe dynamic e l a s t i c i t y in ar t e r i e s by using a s t r a i n increment (£inc) based on the mean radius at which the increment occurs,('R ), rather than the i n i t i a l unstressed radius (Ro) (Bergel, 1961a, 1972; Mcdonald, 1974): € inc = AR/K (4.17) An incremental e l a s t i c modulus (Eine) i s defined for uniaxial extension as: Ein c [ l ] = A<5~/€inc = (1+6) (4.18) Note that Eine is related to the tangential modulus E by the factor O+O, since K = Ro(1+e). 109 The dynamic incremental modulus could be calculated from o s c i l l a t o r y i n f l a t i o n (biaxial) data by substituting £inc for A£ in equations 4.12 and 4.13. An alternative and easier c a l c u l a t i o n of Einc from i n f l a t i o n data i s possible i f the change in length which accompanies the circumferential s t r a i n increment is zero, or n e g l i g i b l y small (Bergel, 1961a; Dobin and Doyle, 1970; Milnor, 1982). Under these conditions, Einc [2] = (1- VZ) A<T/£inc = (1+ d ) (1- V 2 ) (4.19) In the experiments reported here, the dynamic incremental modulus E* is determined for the circumferential d i r e c t i o n by using equation 4.18 with uniaxial data, and equation 4.19 with b i a x i a l data. 110 C. EXPERIMENTAL METHODS Live specimens of Octopus d o f l e i n i , from 10 to 15 kg. in weight, were obtained from scuba divers near Tofino, B r i t i s h Columbia, and from box traps set near Tacoma, Washington. Both s i t e s are areas where th i s species occurs in great abundance. The animals were kept in a r e c i r c u l a t i n g sea water system at 10 degrees C. ( s a l i n i t y of 28 parts per thousand), and fed on a diet of frozen f i s h , l i v e crabs and bivalve molluscs. A l l experiments were performed in v i t r o on segments of the dorsal aorta (Fig.1.1), excised from octopuses under cold anaesthesia. The samples were washed and stored in cold saline (0.4 um f i l t e r e d sea water) containing 1% of a p e n n i c i l l i n + streptomycin + fungizone solution (Gibco Labs.) Most tests were done at 10 degrees C, although in a few cases room temperature (20 degrees C) was used instead. No differences in the passive mechanical response of the aortae could be detected between these temperatures. 1 . I n f l a t i o n Experiments A schematic diagram of the apparatus used for both quasi-static and dynamic i n f l a t i o n tests i s shown in Figure 4.3. Artery segments about 5 cm long were cannulated at one end with a tubular metal connector of appropriate diameter and held in the saline f i l l e d chamber. This connector was linked to a saline pressure reservoir and either a linear infusion pump for qua s i - s t a t i c tests or to a sinusoidal pump I l l Dynamic Static P.D F i g u r e 4.3. Diagram of the i n f l a t i o n apparatus. The a r t e r y sample i s h e l d i n a t i s s u e bath and i n f l a t e d e i t h e r by a l i n e a r pump (LP) or a s i n u s o i d a l pump (SP) powered by a v i b r a t o r (V). The pre s s u r e i n s i d e the a r t e r y i s measured by a pressure transducer (PT) and the diameter of the a r t e r y i s measured by e i t h e r a video dimension a n a l y s e r (VDA) or a c a n t i l e v e r d e v i c e (LVDT). Q u a s i - s t a t i c pressure and diameter data are recorded on a s t r i p c h a r t (C). Pressure and diameter s i g n a l s i n dynamic t e s t s are r e s o l v e d i n t o amplitude (R) and phase (©) by a t r a n s f e r f u n c t i o n a n a l y s e r (TFA). A = power a m p l i f i e r ; PH = pressure head; SG = s i g n a l g enerator. 1 1 2 for dynamic tests. The blood vessel was perfused with saline to clear any a i r bubbles from the system. The d i s t a l end of the specimen was then l i g a t e d . This arrangement l e f t the artery free to lengthen as i t was i n f l a t e d . Artery segments were usually taken from the portion of aorta between the heart and the digestive gland where no branch vessels were present (Fig. 1.1). In some cases the d i s t a l portion of the aorta, at about the l e v e l of the crop, was used for i n f l a t i o n and branch vessels were l i g a t e d . Leak-free preparations were normally obtained without d i f f i c u l t y . A preconditioning time of about 30 minutes was allowed, during which the vessel segment was subjected to periods of c y c l i c i n f l a t i o n and exposed to a st a t i c pressure head of 80 to 100 cm of water. Following this treatment, quasi-static pressure-volume curves were generated by very slow, continuous cycles of i n f l a t i o n and de f l a t i o n of the vessel segment by the linear pump. The pump consisted of a cali b r a t e d glass syringe with a spring-loaded piston which could be advanced or retracted at a pre-determined rate by a reversible, variable speed motor (Cole-Parmer Master Servo-Dyne). A cycle consisted of taking the artery from zero pressure to about 100 cm of water and back to zero. Infusion rates varied from 10 to 15 m i c r o l i t r e s per second, depending on the specimen size, so that each cycle took two to three minutes. For a t y p i c a l specimen at zero pressure, r = 0.115 cm, R = 0.225 cm and L = 3.5 cm. The cycles were repeated u n t i l stable P-V curves were obtained. 1 1 3 Transmural pressure was measured through an 18 gauge needle which was glued into the artery connector and coupled to a BioTec BT70 pressure transducer by a short length of polyethylene tubing (PE 190). Changes in the external diameter or length of the artery were determined with a non-contact measuring system, consisting of a video camera and monitor (RCA-TC1000) and a video dimension analyser (Instruments for Medicine and Physiology, V.D.A. 303) The VDA provides an analog voltage signal which is proportional to the distance between two reference points on the object being displayed on the monitor. Details of the theory and operation of the VDA are given by I n t a g l i e t t a and Tompkins (1972). The dimension measurement i s made on the horizontal axis of the t e l e v i s i o n and has a resolution of about 0.1% of the f u l l width of the screen (Fung, 1981). Since the infusion rates were constant in each experiment a c a l i b r a t i o n of the pump allowed the time axis of the data recording to be read in units of volume increment. This method of volume measurement r e l i e s on a leak-free vessel. By comparing the volume delivered to the volume withdrawn during one cycle the presence of leaks in a preparation could be detected. Experiments to demonstrate the effect of muscle act i v a t i o n on the mechanical behaviour of the artery wall were ca r r i e d out using 5-HT (5-hydroxy-tryptamine:creatin sulfate complex, Sigma Co.) as a stimulatory agent and ACh (acetyl-choline chloride, Sigma Co.) as a muscle relaxant. Drugs were dissolved in saline and introduced into the artery 1 1 4 lumen by infusion after opening the d i s t a l l i g a t u r e . As the drug solution flowed through the vessel i t was allowed to mix into the surrounding bath. The ligature was then closed and the artery was i n f l a t e d , using the same drug solution in the pump. Stress-relaxation tests were performed by rapidly i n f l a t i n g the vessel to a given pressure, then stopping the pump (braking time <20 milliseconds) and following the pressure decrease inside the specimen with time. Dynamic i n f l a t i o n experiments involved measuring small pressure and diameter o s c i l l a t i o n s over a frequency range of 0.05 to 10 Hz. These experiments were carried out on artery segments at three d i f f e r e n t mean pressures: 30, 35 or 60 cm of water (corresponding to circumferential strains of approximately 0.6, 1.0, 1.2 respectively). Small sinusoidal volume changes were imposed on the i n f l a t e d artery by a diaphragm pump driven by an electromagnetic vibrator (Ling Systems 200). The amplitude and frequency of the vibrator were controlled by a signal generator which also provided the reference signal for a phase analyser. A needle valve inserted between the pump and the s t a t i c pressure head ensured that flow from the pump back into the reservoir would be negligible (see F i g . 4.3). The volume amplitude was adjusted to give diameter changes of less than +/-5% of the mean value. Under these conditions the pressure (P) and diameter (D) o s c i l l a t i o n s were sinusoidal with l i t t l e d i s t o r t i o n , and P-D hysteresis loops were es s e n t i a l l y l i n e a r . The amplitudes and the phase s h i f t (3) 1 15 between P and D signals at each frequency were measured by the phase analyser (SE Labs SM272DP Transfer Function Analyser) as described by Denny and Gosline (1980). The P and D signals were also recorded continuously on a two channel s t r i p chart recorder. The frequency response c h a r a c t e r i s t i c s of the pressure transducer were tested by a free-vibration method using a step function of pressure ("pop" test, Gabe, 1972). The transducer and P.E. tubing system together had a damped resonant frequency of 45 Hz, and a damping factor of 0.26. Over the frequency range used the pressure signal was delayed by 0.7 degree per Hz, and had an amplitude error of less than 4% at 10 Hz. The VDA output i s processed through an internal single RC 15 Hz f i l t e r , which at 10 Hz gives a 25% attenuation and a .135 degree phase lag. Corrections to the VDA signal were made from frequency response data for t h i s instrument, as measured by the phase analyser. In some experiments, prior to the a v a i l a b i l i t y of the VDA, the diameter changes were measured with a mechanical displacement transducer. This consisted of a lightweight pivoting arm with a s l i g h t l y curved foot which rested against the upper surface of the artery and moved up and down with d i l a t i o n s of the vessel. The arm movements were monitored with a Linearly Variable Differential Transformer (Shaevitz 050MHR-LVDT). The pivot arm exerted a force against the artery wall of-less than 1 gram over a foot area of 0.5 cm7" . Measurements made with t h i s device were in good agreement 1 1 6 with the results of experiments using the VDA. At the end of each qua s i - s t a t i c or dynamic i n f l a t i o n experiment the unstressed length and external radius were recorded. Next, the wall thickness was determined from measurements of thin, freshly cut cross-sections of the vessel, by using a f i l a r micrometer on a dissecting microscope. The vessel wall volume was calculated on the basis of a uniform c y l i n d r i c a l geometry and assuming isovolumetric deformation. This allowed a determination of vessel length, L, and inside radius, r, from -A V and R at any pressure (or R and r from A V and A L ) . Equations 4.5 to 4.8 were used to obtain b i a x i a l s t r e s s - s t r a i n curves. Values of tangential e l a s t i c moduli were computed from eqn. 4.12 and 4.13 by the procedure of Dobrin and Doyle (1970; see A n a l y t i c a l Methods). Dynamic pressure and radius data were used with eqn. 4.19 to obtain values of the incremental e l a s t i c modulus for the circumferential d i r e c t i o n . 2. Uniaxial Force-Extension Tests Quasi-static uniaxial tests of the circumferential e l a s t i c properties were carr i e d out by slowly stretching short pieces of aorta (3 to 4 mm long) as intact rings on a t e n s i l e testing machine (Instron model 1120). The rings were mounted over two r i g i d L-shaped st a i n l e s s steel bars, one of which was secured to the base of the test frame, while the other one was attached to a force transducer on the moveable cross-head (Fig. 4.4A). The force transducer was a single 117 beam strain-gauge type which gave r e l i a b l e measurements of forces from about 0.1 to 500 grams. This transducer was ca l i b r a t e d by hanging known weights from the beam. Extension of the sample was measured e l e c t r o n i c a l l y by continuous monitoring of the position of the cross-head of the Instron. The ring samples become flattened under a force of less than 1 g and therefore could be considered as two p a r a l l e l sheets of tissue, each having a length equal to one-half of the circumference of the loop. Thus, uniaxial extension of the ring samples gave stresses which were e s s e n t i a l l y in the circumferential d i r e c t i o n (Attinger, 1968; Goedhard and Knoop, 1973). Force-extension data were recorded on the X-Y plotter of the Instron. Force-extension tests were conducted on the artery rings by slow c y c l i c stretching at crosshead speeds which ranged between 0.5 and 5 mm/min. This gave corresponding st r a i n rates of approximately 0.002 to 0.02 per second. No differences in the response of the artery specimens was detected within the range of s t r a i n rates used. In these tests, as in the i n f l a t i o n experiments, i t was necessary to precondition the artery sample afte r i t had been held in the unstressed state. During the experiments the samples were immersed in a saline bath at 10 degrees C. In another series of experiments the longitudinal e l a s t i c properties of the aorta were investigated. Vessel segments about 5 cm long were mounted in the saline bath by l i g a t i n g the ends over tubular connectors which were attached 118 force 10°C a base B force 10° C base F i g u r e 4.4. Diagram of the u n i a x i a l t e s t specimens i n the I n s t r o n machine. A) Ring samples cut from a r t e r i e s ( a ) , were mounted over two s t i f f L-shaped bars, one of which was atta c h e d to the f o r c e transducer on the moveable crosshead of the I n s t r o n , and the other of which was f i x e d to the s t a t i o n a r y base. B) L o n g i t u d i n a l t e s t s were made on segments of the a o r t a (a) which were g r i p p e d at each end by t y i n g over f l a r e d cannula tubes. The lower tube has a small hole i n the sid e to allow p r e s s u r e e q u a l i s a t i o n between the chamber bath and the v e s s e l lumen. 119 to the Instron test frame (Fig. 4.4B). The samples were subjected to longitudinal force-extension tests by following the same procedure described for the ring samples. A hole through one connector allowed f l u i d movement in and out of the vessel lumen, thus maintaining the transmural pressure at zero throughout the test. Sample dimensions were measured at the end of each test as described above. Strain c a l c u l a t i o n s were based on an unstressed sample length which was measured at the crosshead position where a positive force was f i r s t recorded. For stress calculations the cross-sectional area of rings was taken as 2hL (see F i g . 4.2A), and for the longitudinal samples i t was IT (R x - r 1"). By assuming that deformation was isovolumetric the cross-sectional area at each s t r a i n could be calculated from the i n i t i a l dimensions. Dynamic mechanical tests were also conducted on artery ring samples by using a forced s t r a i n o s c i l l a t i o n technique which was analogous to the dynamic i n f l a t i o n . Ring samples were loaded to predetermined strains and then subjected to small sinusoidal s t r a i n increments at 0.1 to 10 Hz, by an electromagnetic vibration apparatus (Gosline and French, 1979). Deformation of the sample was measured by a st r a i n guage displacement transducer attached to the vibrator shaft. Force was measured by a semiconductor s t r a i n gauge transducer which was linked, by the sample, to the vibrator. Experiments were performed at mean strains of 0.30 and 0.60. The displacement amplitude was kept small enough (+/-2% of the 120 mean strain) to give r e l a t i v e l y • linear force-extension hysteresis loops. Force and displacement signals were conditioned with matched c a r r i e r amplifiers (SE Labs type 4300), and the amplitudes and phase relationship measured by the Transfer Function Analyser. The resonant frequency of the force transducer was 2 orders of magnitude greater than the highest test frequency and therefore no signal corrections were necessary. The force and extension data were used to calculate the dynamic incremental modulus, according to equation 4.18. 121 D. RESULTS 1. I n f l a t i o n Experiments In v i t r o i n f l a t i o n of the octopus aorta demonstrated that the vessel i s a highly d i s t e n s i b l e e l a s t i c tube. Figure 4.5 shows a t y p i c a l set of consecutive i n f l a t i o n d e f l a t i o n curves for an aortic segment. The f i r s t i n f l a t i o n curve i s highly sigmoid and l i e s well above the def l a t i o n curves. Since the product of pressure (P) and volume (V) is work, then the area under the i n f l a t i o n curve i s the t o t a l work done or the energy used in distending the artery, while the area under the deflation curve i s the energy recovered by e l a s t i c r e c o i l . The area enclosed by the P-V loop i s the energy lost as heat through viscous processes and, when expressed as a fraction of the t o t a l energy, i s c a l l e d the mechanical hysteresis. For the f i r s t i n f l a t i o n cycle shown in Figure 4.5 the hysteresis was 43%. With subsequent i n f l a t i o n s the curves were shifted to the right and the hysteresis loops became smaller. Three to four cycles were normally enough to obtain a stable response with 25% to 30% hysteresis. The apparent i n s t a b i l i t y of hysteresis curves during the f i r s t few str a i n cycles is a phenomenon which i s t y p i c a l of vertebrate a r t e r i e s tested in v i t r o (Remington, 1955; Bergel, 1961a; Fung, 1972). The process of "preconditioning" the specimen to attain the steady state response i s regarded'as a necessary period of "adjustment" of the internal structure after the artery has undergone the mechanical trauma of being excised and allowed to experience an e s s e n t i a l l y unstressed 122 0 0.2 0.4 0.6 Volume (ml) Figure 4 . 5 . Quasi-static pressure-volume curves for a segment of aorta. The inflation curves (solid lines) and deflation curves (broken lines) for the f i r s t four successive tests are shown, as indicated by the numbers, to illustrate the effect of preconditioning the specimen. Arrows indicate the direction of loading. 123 state (Fung, 1972). The most important feature of the P-V curves i s that the volume d i s t e n s i b i l i t y of the aorta, (dV/VdP), decreased continuously with distension in the physiological range of blood pressures (approximately 20 to 50 cm of water). In a l l i n f l a t i o n experiments the artery segments were free to lengthen when pressurised. This condition mimics the in vivo state. In contrast to the situation in mammals, the octopus i s a soft-bodied invertebrate and the aorta i s not r e s t r i c t e d to a fixed length in vivo by tethers to a r i g i d s k e l e t a l framework. I n f l a t i o n of the octopus aorta always resulted in an increase in length as well as in circumference. The changes in these dimensions which occurred in a t y p i c a l set of experiments are shown in Figure 4.6. Here, at a pressure of 50 cm of water the increase in length was 30% (£l = 0.30), while the circumference had increased by 120% (€c = 1.20). Since volume increases with the square of the radius, but l i n e a r l y with vessel length, i t can be seen that the circumferential s t r a i n contributes the major portion of the volume d i s t e n s i b i l i t y of the aorta. Above physiological pressures only r e l a t i v e l y small changes in longitudinal and circumferential s t r a i n were observed. The aorta has a r e l a t i v e l y thick wall at zero pressure, the r a t i o h/R being about 0.45. However, due to the large circumferential strains, at 50 cm of water pressure h/R i s reduced to about 0.11. In mammalian ar t e r i e s h/R i s about 0.10 at zero pressure and decreases to about half of this 124 0 .2 .4 .6 .8 1.0 1.2 Strain £ F i g u r e 4.6 R e s u l t s of q u a s i - s t a t i c pressure-volume t e s t s , expressed i n terms of the s t r a i n i n circumference (£c) and i n l e n g t h (€1). The approximate upper and Lower p h y s i o l o g i c a l p r e s s u r e s are i n d i c a t e d by the broken l i n e s . 125 value at physiological pressures (Dobrin, 1978). Figure 4.7 presents i n f l a t i o n data, taken from the ascending limb of P-V loops ( i . e . the loading curve), in terms of stress and st r a i n in the circumferential and longitudinal d i r e c t i o n s . The observed s t r e s s - s t r a i n relations for the octopus aorta were always non-linear, just as is t y p i c a l l y seen for the a r t e r i e s of vertebrates. The circumferential s t r e s s - s t r a i n data for segments taken from the aorta at the le v e l of the crop (curve c )indicate that in this region (see F i g . 1.1) the aorta i s somewhat less extensible than the main part of the vessel which l i e s proximal to this s i t e (curve d). Likewise, the longitudinal e x t e n s i b i l i t y of the aorta appears to be less in the d i s t a l segments than in the proximal ones. While these differences in e x t e n s i b i l i t y may indicate the presence of an " e l a s t i c taper" in the aorta, as i s known to occur in the vertebrate aorta (see McDonald, 1974), t h i s p o s s i b i l i t y was not investigated further in this study. The experiments to follow deal only with the major proximal portion of the aorta which is characterised by curves b and d in Figure 4.7. 2. Activation of Vascular Muscle Immediately after excision, many aortae exhibited a brief period of spontaneous muscle a c t i v i t y which was severe enough to cause v i s i b l e undulatory movements along the length of the vessel. However this phenomenon did not pers i s t for more than about t h i r t y minutes in cold saline. Spontaneous 126 .6 .8 Strain € F i g u r e 4 . 7 I n f l a t i o n data, taken from ascending limb of q u a s i - s t a t i c p r e s s u r e volume curves and computed as s t r e s s and s t r a i n i n the l o n g i t u d i n a l d i r e c t i o n f o r d i s t a l (a) and proximal (b) p o r t i o n s of the a o r t a , and i n the c i r c u m f e r e n t i a l d i r e c t i o n f o r d i s t a l (c) and promimal (d) p o r t i o n s of the a o r t a . Number of ao r t a e samples, N = 8 f o r (a) and ( c ) ; N = 5 f o r (b) and ( d ) . 1 27 muscle a c t i v i t y was also indicated by b r i e f , large pressure transients or by small pressure pulsations which occasionally occurred during the slow i n f l a t i o n of a vessel. This a c t i v i t y appeared to be abolished by several consecutive i n f l a t i o n cycles during the normal preconditioning period, or by exposure of the artery to a high pressure (100 cm of water) for several minutes. A similar procedure has been used to cause relaxation of the muscles in mammalian a r t e r i e s (Cox, 1978) . Since the main objective of this study was to measure the passive mechanical properties of the artery wall, i t was necessary to be able to d i s t i n g u i s h between the active and relaxed states of the vascular muscle. To do t h i s , drugs were used which have previously shown excitatory or i n h i b i t o r y e f f e c t s on the octopus c i r c u l a t i o n in vivo (Johansen and Huston, 1962) or on the aorta in v i t r o (Wells and Mangold, 1980). Prolonged periods of muscle act i v a t i o n ( i . e . several minutes) could be produced by treatment with 5-Hydroxytryptamine. Figure 4.8 shows the results of an experiment in which a preconditioned a o r t i c segment was subjected to 3 sets of i n f l a t i o n s , the f i r s t with normal saline (a), the "second after infusion with 5HT (b), and the t h i r d following infusion with acetylcholine (c). P-V curves for the control and acetylcholine treated artery are v i r t u a l l y i d e n t i c a l . In the presence of 5HT however, the volume d i s t e n s i b i l i t y of the aorta was greatly reduced, p a r t i c u l a r l y over the physiological range of pressures. These 128 0 2 M .6 .8 U) 1.2 A V (ml.) Figure 4.8. Quasi-static i n f l a t i o n of an a o r t i c segment under control conditions (a, broken l i n e ) , following infusion o f 5-hydroxytryptamine at 100 ug/ml concentration (curve b), and following infusion of acetylcholine at a concentration of 1 . 0 mg/ml (curve c ) . 129 results suggest that the muscle in the preconditioned, control artery i s in the relaxed state. Thus, the results of other mechanical tests on preconditioned artery samples, where drugs were not used, may be regarded as representing the passive e l a s t i c properties of the vessel wall. The hysteresis observed for the i n f l a t i o n of the octopus aorta with activated muscle (28%) was only s l i g h t l y higher than the hysteresis for that p a r t i c u l a r vessel under control conditions (22%, Fig . 4.8). In quasi-static i n f l a t i o n of mammalian a r t e r i e s , hysteresis i s usually increased by act i v a t i o n of the vascular muscle (Dobrin, 1973; Busse et a l . , 1981; Bauer et a l . , 1982; Milnor, 1982), but to a degree which varies with the anatomical o r i g i n of the artery. In "muscular" a r t e r i e s , such as the carotid, muscle activation causes a greater increase in hysteresis than occurs with ac t i v a t i o n in the " e l a s t i c " aorta (Busse et a l . , 1981). Stress-strain curves for the loading portion of the P-V curves in Figure 4.8 are shown in Figure 4.9A (longitudinal direction) and Figure 4.9B (circumferential d i r e c t i o n ) . Here, st r a i n i s expressed with reference to the i n i t i a l dimensions of the relaxed vessel. Note that 5HT did not produce a measureable change in the external diameter at zero pressure (although the length appeared to increase by about 6%). In mammalian a r t e r i e s , muscle activation t y p i c a l l y causes c o n s t r i c t i o n of 25% to 30% in the carotid, 10% to 12% in the abdominal aorta, and somewhat less in the thoracic aorta (Remington, 1962; Dobrin and Doyle, 1970; Gow, 1972; Busse et 130 F i g u r e 4.9. S t r e s s - s t r a i n curves f o r the l o a d i n g p o r t i o n of the pressure-volume curves i n F i g u r e 4.8, f o r l o n g i t u d i n a l (A) and c i r c u m f e r e n t i a l (B) d i r e c t i o n s . S t r a i n i s g i v e n i n terms of the i n i t i a l dimensions of the r e l a x e d v e s s e l . A c t i v a t i o n of muscle i n c r e a s e d the s t r e s s i n the a r t e r y w a l l . The " a c t i v e s t r e s s " i s p l o t t e d as the d i f f e r e n c e between curves f o r 5-HT and ACh treatments and i s l a b e l l e d D. The broken p a r t of the a c t i v e s t r e s s curve i s c a l c u l a t e d from e x t r a p o l a t i o n of the 5-HT curve to i n t e r s e c t with the ACh c u rve. 131 a l . , 1981). For a l l values of s t r a i n in the octopus aorta, the circumferential and longitudinal stresses were elevated by activation of the muscle (with the exception of the i n i t i a l part of the longitudinal extension). The difference between the stress curves for the stimulated and relaxed states is c a l l e d the active stress component, and t h i s i s plotted in Figures 4.9A and 4.9B. Active stress in the circumferential d i r e c t i o n increased continuously with s t r a i n , reaching an apparent peak at €c = 1.0. In the longitudinal d i r e c t i o n , the active stress increased to a plateau l e v e l at €1 > .20. These results suggest, as might be expected, that the magnitude of the active stress response is maximal at some optimum circumference or length. The data in Figure 4.9 indicate that t h i s optimum dimension occurs at circumferential and longitudinal strains that correspond to a pressure of about 35 cm of water which is in the middle of the physiological range. These results are consistent with observations on the active stress response of mammalian vascular muscle (Cox, 1978;, Dobrin, 1978). 3. Uniaxial Tests Figure 4.10 shows t y p i c a l force-extension curves obtained from qua s i - s t a t i c uniaxial tests of the aorta in the longitudinal (a) and circumferential (b) d i r e c t i o n s . Hysteresis, calculated from these curves, was greater in longitudinal extension (39%) than in circumferential extension (26%). These values are similar to what was observed for i n f l a t i o n of vessel segments. Data from the load 132 Extension (mm) F i g u r e 4.10. T y p i c a l f o r c e - e x t e n s i o n curves obtained from q u a s i - s t a t i c u n i a x i a l t e s t s of the a o r t a i n the l o n g i t u d i n a l (A) and c i r c u m f e r e n t i a l (B) d i r e c t i o n s . H y s t e r e s i s i s 39% i n (A) and 26% i n (B). 1 33 portion of force-extension curves for several aortae are plotted as stress and s t r a i n in Figure 4.11. These curves resemble the J-shaped s t r e s s - s t r a i n curves obtained from b i a x i a l (i.e i n f l a t i o n ) tests, with the exception that in uniaxial tests the artery wall i s more extensible, p a r t i c u l a r l y at high stresses in the circumferential d i r e c t i o n . Values of the tangential e l a s t i c moduli, E l and Ec, were calculated d i r e c t l y from the uniaxial s t r e s s - s t r a i n curves using equation 4.4 and the results are shown in Figure 4.12. Over the range of extensions used the artery wall increased in s t i f f n e s s by approximately 2 orders of 3 5 x magnitude, i . e . E l varies from 3 X 10 to 1.8 X 10 N/m while Ec varies' from about 5 X 1 0 to 5 X 1 0 N/m These values of modulus are c h a r a c t e r i s t i c of an e l a s t i c material which has between 1/200 and 1/2 the s t i f f n e s s of an ordinary rubber band. The dramatic increase in e l a s t i c modulus with s t r a i n is in agreement with the decreased volume d i s t e n s i b i l i t y observed at high pressures (Figure 4.5). 4. Calculation of Ec from I n f l a t i o n Data Although uniaxial tests on isolated artery rings are simple, convenient, and reasonably useful at low s t r a i n s , results from these tests at large strains are not necessarily r e l i a b l e because the f i b r e orientation within the vessel wall must be quite d i f f e r e n t in uniaxial versus b i a x i a l specimens, p a r t i c u l a r l y at high s t r a i n s . Thus, i t was desirable to calculate the circumferential e l a s t i c modulus 134 0 .U .8 1.2 1.6 Strain F i g u r e 4.11. Load p o r t i o n of f o r c e - e x t e n s i o n curves f o r s e v e r a l a o r t a e , p l o t t e d as s t r e s s and s t r a i n f o r the c i r c u m f e r e n t i a l and l o n g i t u d i n a l d i r e c t i o n s . Each curve i s a r e g r e s s i o n on 20 t r i a l s . 135 F i g u r e 4.12. T a n g e n t i a l e l a s t i c moduli, E l and Ec c a l c u l a t e d from the u n i a x i a l s t r e s s - s t r a i n data i n F i g u r e 4.11, a c c o r d i n g to equation 4.4. Modulus i s p l o t t e d on a l o g a r i t h m i c s c a l e . Curves are drawn through the data from polynomial r e g r e s s i o n a n a l y s i s . 136 from b i a x i a l i n f l a t i o n data. This procedure, as described above, requires the knowledge of either Poisson's r a t i o or the longitudinal modulus. Since Poisson's ra t i o s were not measured d i r e c t l y , i t was decided to use values of E l from uni a x i a l tests in order to determine V c l and Ec from the b i a x i a l data. To do t h i s , i t must be assumed that the u n i a x i a l E l values are close to the true b i a x i a l values. The assumption seems reasonable since the uniaxial longitudinal tests involved only small strains (up to 30%) which probably did not cause too extensive an a l t e r a t i o n in fibr e o r i e n t a t i o n . F i r s t , values of V c l were calculated from eqn. 4.13; these ranged between 0.2 and 0.54, and had a mean of 0.30. Next, the V c l values were used in eqn 4.12 to solve for Ec at d i f f e r e n t circumferential s t r a i n s . The circumferential e l a s t i c modulus, Ec calculated from b i a x i a l data, i s plotted in Figure 4.13 as a function of pressure, and in Figure 4.14 as a function of str a i n (curve a). Ec has the same range of magnitude as determined from the uni a x i a l data (Fig. 4.12), with values at the lower and upper 3 physiological pressures being approximately equal to 9 X 10 5" 2. and 2.3 X 10 N/m , respectively. For these data, the approximate physiological range of pressures correspond to circumferential strains of 0.5 to 1.18. The r a t i o of moduli, (Ec/El), varies with pressure between 1.05 and 3.30 (Fig. 4.13). Thus, i t appears that the octopus aorta has greater s t i f f n e s s circumferentially than l o n g i t u d i n a l l y at a l l pressures, and has a Poisson's r a t i o which is generally less 1 3 7 6 10F Pressure (cm H 2 0) F i g u r e 4.13. C i r c u m f e r e n t i a l modulus of e l a s t i c i t y , Ec, p l o t t e d as a f u n c t i o n of i n f l a t i o n p r e s s u r e . The r a t i o of c i r c u m f e r e n t i a l modulus to l o n g i t u d i n a l modulus ( E c / E l ) i s a l s o shown. P o i n t s r e p r e s e n t means, and bars are +/- one standard e r r o r . Arrows i n d i c a t e the approximate upper and lower p h y s i o l o g i c a l range of i n v i v o blood p r e s s u r e . 138 F i g u r e 4.14. C i r c u m f e r e n t i a l e l a s t i c modulus Ec as a f u n c t i o n of s t r a i n , c a l c u l a t e d from b i a x i a l i n f l a t i o n data ( a ) , and a l s o from u n i a x i a l f o r c e - e x t e n s i o n data (b; redrawn from F i g . 4.12). V e r t i c a l bars are one standard d e v i a t i o n f o r ( a ) . Arrows on the a b c i s s a are the approximate s t r a i n s f o r p r e s s u r e s of 20 and 50 cm of water. 1 39 than 0.5. Under these conditons equation 4.13 yields positive values of A^-l, that i s , the artery should lengthen as i t i s i n f l a t e d . Mechanical anisotropy has also been described in many mammalian a r t e r i e s . In the dog, E l > Ec for the thoracic aorta (Patel et a l . , 1969), while Ec > E l in the c a r o t i d artery (Dobrin and Doyle, 1970; Cox, 1975). In Figure 4.14, the curve for Ec, as calculated from uniaxial extension, i s redrawn for comparison to Ec values determined from i n f l a t i o n t e sts. For strains below 1.10, tests on ring samples gave values of Ec which are in close agreement with those obtained from i n f l a t i o n of vessel segments. At strains above 1.10 the two curves diverge. As explained above, ring samples may be expected to show mechanical behaviour which i s d i f f e r e n t from the intact vessel, p a r t i c u l a r l y at high extensions, because the artery wall i s not a homogeneous material. At large strains i t i s l i k e l y that f i b r e networks in the artery wall w i l l be reoriented considerably, in ways which may d i f f e r in the two types of samples. Since these a n a l y t i c a l methods are not exact, the results must be regarded as only approximations of the real values. It i s quite s a t i s f y i n g , therefore, that uniaxial and b i a x i a l tests on the aorta gave similar values of Ec for strains which include the physiological range. These results support the use of u n i a x i a l . t e s t s on ring samples for extensions up to about 100%. 140 5. V i s c o e l a s t i c Properties The presence of a s i g n i f i c a n t viscous component in the octopus artery wall was i n i t i a l l y indicated by the hysteresis of the quasi-static P-V curves. In other experiments where stepwise volume changes were imposed on vessel segments, the phenomena of stress-relaxation and stress-recovery were consistently observed. Typical results from one of these experiments are shown in Figure 4.15. The artery wall exhibited both instantaneous ( e l a s t i c ) and time-dependent (viscous) responses to changes in s t r a i n . With each increase in volume the pressure increased i n i t i a l l y , but subsequently decayed as a function of time (stress-relaxation), while with each decrease in volume, the pressure i n i t i a l l y dropped and then slowly increased with time (stress-recovery). Stress-relaxation experiments readily i l l u s t r a t e that the artery wall has time dependent e l a s t i c properties. Since a r t e r i a l v i s c o e l a s t i c i t y is important in determining hemodynamic relationships, i t i s most useful to characterise these properties in terms of frequency, by dynamic testing. A quantitative analysis of the frequency dependent e l a s t i c properties of the octopus aorta i s presented here, based on the combined results of dynamic mechanical tests on intact vessel segments and ring samples. In these tests small sinusoidal strain o s c i l l a t i o n s were superimposed on d i f f e r e n t lev e l s of pre-strain as i l l u s t r a t e d by Figure 4.16A. Examples of a pressure-radius loop from a dynamic i n f l a t i o n experiment and a force-extension loop from artery ring vibration test 141 j I l i i I l 1 1 1 2 k 6 8 10 Minutes F i g u r e 4.15. S t r e s s - r e l a x a t i o n and s t r e s s - r e c o v e r y i n an i n f l a t e d a o r t i c segment. Stepwise volume changes are made and the r e s u l t i n g pressure i s followed with time. 142 are shown in Figures 4.16B and 4.16C, respectively. In both cases, i t can be seen that the str a i n increments were s u f f i c i e n t l y small that these loops were approximately l i n e a r . Figure 4.17A shows that the storage modulus E' increased continuously with the frequency of o s c i l l a t i o n for each l e v e l of pre-strain which was tested. In addition, the proportional change in E' over the range of frequencies used increased with s t r a i n , i . e . , the r a t i o of E' at 10 Hz to E' at 0.1 Hz was 1.33 at £ c = 0.3 (curve d ), 1.43 at €c = 0.6 (curve c ) , 1.88 at C c = 1.0 (curve b) and 1.96 at £ c = 1.2 (curve a) . In a l l experiments, the phase angle S was pos i t i v e ( i . e . the change in pressure or force always led the change in radius or extension), and tan S varied between 0.11 and 0.27 (Fig. 4.17B). For these values of 6 , E' is approximately equal to E* (equation 4.14; see table 4.1). Unlike E', tan 6 did not seem to change s i g n i f i c a n t l y with d i f f e r e n t l e v e l s of pre-strain, except perhaps at the highest frequencies when curves for lower pre-strain (a and b) appear to diverge from curves for higher pre-strain (c and d). With increasing frequency there was a steady r i s e in tan S , and t h i s indicates that the loss modulus E'' was increasing r e l a t i v e to E'' (since tan 5 = E''/E'). In other words, although more e l a s t i c energy was stored at higher rates of deformation, a greater proportion of the energy put into the system was lost through viscous processes. Table 4.1 shows some representative values of the v i s c o e l a s t i c parameters for 143 0 .4 .8 ^2 Strain F i g u r e 4.16. Diagram to i l l u s t r a t e dynamic mechanical t e s t i n g of the a o r t a . Small s i n u s o i d a l o s c i l l a t i o n s of s t r a i n are imposed at d i f f e r e n t l e v e l s of p r e - s t r a i n , as shown i n (A). Examples of a p r e s s u r e - r a d i u s loop from a dynamic i n f l a t i o n experiment (B), and a f o r c e - l e n g t h loop from a v i b r a t i o n t e s t (C), both at f r e q u e n c i e s of 1 Hz are shown. 144 O L — i — i — i i i 1111 1 i i i i 1111 • • * i i i i 11 .1 1 10 Frequency (Hz) F i g u r e 4.17. R e s u l t s of dynamic mechanical t e s t s on the a o r t a , p l o t t e d as storage modulus, modulus, E' (panel A), and l o s s tangent, tan d (panel B), as f u n c t i o n s of frequency. Curve a: mean pressure of 60 cm of water ( p r e - s t r a i n =1.2). Curve b: mean pressure of 40 cm of water ( p r e - s t r a i n - 1.0). Curve c: mean pressure of 30 cm of water ( p r e - s t r a i n = 0.6). Curve d: v i b r a t i o n t e s t s o n l y , p r e - s t r a i n = 0.3. 1 45 experiments in which mean st r a i n was in the middle of the physiological range (£c = 1.0). The dynamic v i s c o s i t y n' decreased steadily from 0.1 to 10 Hz, as i s c h a r a c t e r i s t i c of a crosslinked v i s c o e l a s t i c s o l i d (Ferry, 1970). In the f i r s t stage of thi s study mechanical hysteresis was defined as the r a t i o of the energy dissipated to the t o t a l energy used through one cycle of deformation. The ef f i c i e n c y of e l a s t i c energy storage may be expressed as the re s i l i e n c e Re, where Re i s the r a t i o of energy recovered in e l a s t i c r e c o i l to the t o t a l energy input. Thus, Re = 1-H, where H i s the hysteresis. It was shown in quasi-static s t r e s s - s t r a i n tests (Fig. 4.5, 4.8 and 4.10) that the octopus aorta exhibited hysteresis of about 25% to 30%; t h i s corresponds to a r e s i l i e n c e of 70% to 75%. In v i s c o e l a s t i c materials the r e s i l i e n c e usually decreases with increasing frequency. Tan 6 is proportional to the r a t i o of energy lost to energy stored in one cycle of a sinusoidal o s c i l l a t i o n . For linear s t r e s s - s t r a i n o s c i l l a t i o n s the hysteresis may be calculated as (Wainwright et a l . , 1976): Re = exp(- TV tan 6) (4.20) In dynamic tests at a mean st r a i n of 1.0, Re was 70% at 0.05 Hz (tan 6 = 0.11), 67% at 0.5 Hz (tan & = 0.13) and 62% at 1.0 Hz (tan <S = 0.15). Physi o l o g i c a l l y relevant frequencies of pressure o s c i l l a t i o n s in the aorta of 0. d o f l e i n i range up to about 1.0 Hz (see chapter V). At frequencies above 1.0 Hz tan 6 continued to increase, (Fig. 146 Table 4.1 V i s c o e l a s t i c data for octopus aorta at mean st r a i n of 1.0. E* = complex dynamic modulus E' = storage modulus E" = loss modulus tan 6 = loss tangent n' = dynamic v i s c o s i t y Frequency E* E' E" tan 6 n ' (Hz) (N/m2) (N/m2) (N/m2) (N-sec/m2) 0.1 0.86 0.85 0.107 0.12 0.17 1.0 1.01 0.99 0.15 0.15 0.02 10 1.60 1.55 0.42 0.29 0.007 147 4.17B, curve b), with a concomitant drop in the e l a s t i c energy storage e f f i c i e n c y . The results of the dynamic mechanical tests a l l are consistent with the interpretation that the octopus aorta is a v i s c o e l a s t i c structure, in which the importance of viscous forces in the molecular networks of i t s components increases with the rate of deformation. Thus, at increased frequency, the a o r t i c wall shows an increased s t i f f n e s s and a decreased r e s i l i e n c e . In these two respects the octopus aorta is mechanically similar to the mammalian a r t e r i e s as well as other long-chain polymeric materials. 1 48 E. DISCUSSION 1. Mechanical Properties of the Aorta The octopus aorta has mechanical properties which in general are remarkably similar to the properties exhibited by the a r t e r i e s of vertebrates. The results presented here show that the aorta is a highly d i s t e n s i b l e e l a s t i c tube which appears to be well suited to function as an e l a s t i c reservoir in the central c i r c u l a t i o n . A very important feature of the octopus aorta i s that the e l a s t i c i t y i s highly non-linear. Over the physiological pressure range the passive compliance of the vessel wall i s decreased dramatically as the circumferential e l a s t i c modulus increases from a r e l a t i v e l y low value of about 10^ up to about 2 X 1 0 N/m . This represents a twenty-fold change in the wall s t i f f n e s s through the normal working range of extensions. These results are, q u a l i t a t i v e l y , much l i k e what has been reported for vertebrate a r t e r i e s by many workers. For example, Bergel (1961a) showed that the lumenal volume of the canine thoracic aorta increased by about four times when in f l a t e d from 0 to 300 mm Hg pressure, and the circumferential e l a s t i c modulus increased from 2 X 10 5 to ( 2. about 10 N/m between 80 and 160 mm Hg, the approximate in vivo blood pressure. A l l vertebrate blood vessels that have been studied exhibit "J-shaped" s t r e s s - s t r a i n curves and a progressive increase in wall s t i f f n e s s with extension (or pressure) (Roach and Burton, 1957; Bergel, 1961a; Cox, 1979; 1 49 Fung, 1981). This is apparently a design feature of highly d i s t e n s i b l e pressure vessels which i s necessary in order to prevent i n s t a b i l i t y and rupture (Burton, 1954; Gordon, 1975; Bogen and McMahon, 1980). Burton (1954) showed that for an e l a s t i c tube which is pressurised the volume d i s t e n s i b i l i t y , D (= (dV/VdP), is inversely proportional to ((Eh/R)-P), where E i s the e l a s t i c modulus, h i s the load-bearing area, R is the radius and P is the pressure. As the pressure is raised R w i l l increase and h w i l l decrease. If E remains constant with extension then D w i l l become i n f i n i t e l y large as P approaches Eh/R, and the tube w i l l rupture. This can be avoided either by having E very large r e l a t i v e to P, or by having E increase with radius, such that Eh/R i s always greater than P. In the f i r s t case the tube would be non-compliant (e.g. a steel water pipe), but t h i s would not be very useful as an e l a s t i c reservoir in the c i r c u l a t i o n . The second case i s what has been observed for a l l vertebrate a r t e r i e s as well as the octopus aorta. This allows the vessel to have large compliance at low pressures, thereby smoothing the pulse and o f f e r i n g low resistance to flow from the heart, and yet s t i l l be protected from "blowout" at higher pressures. It follows that the actual values of s t i f f n e s s which the wall of an artery must exhibit, in order to meet the above c r i t e r i a , w i l l depend on the range of physiological pressures normally encountered in that animal, and on the r e l a t i v e thickness of the artery wall with respect to radius 150 (i.e the quantity (Eh/R) must always exceed P). This point i s i l l u s t r a t e d by comparing the octopus aorta to the thoracic aorta of the dog. While the s t i f f n e s s of the both vessels increases dramatically with physiological pressure, the circumferential e l a s t i c modulus i s 10 to 20 times greater in the dog than in the octopus. In the dog, blood pressure i s about 4 times higher, but the r a t i o h/R i s only about one fourth as much as in the octopus aorta. This means that Eh/R maintains the same relat i o n s h i p to pressure in both vessels. In terms of the s t r e s s - s t r a i n behaviour, the aorta of the octopus i s functionally analogous to the aorta of mammals. The passive hysteresis for slow i n f l a t i o n of the octopus aorta i s somewhat higher than what i s t y p i c a l of mammalian a r t e r i e s . It is generally agreed that hysteresis in the artery wall is predominantly a property of the vascular muscle (Dobrin, 1978), although a small degree of hysteresis is also observed in isolated e l a s t i n (Fung, 1981) and collagen (Azuma and Hasewaga, 1973), when tested at low str a i n rates. The magnitude of hysteresis in mammalian ar t e r i e s seems to be well correlated with the r e l a t i v e amount, and degree of a c t i v a t i o n , of vascular muscle (Dobrin, 1978). The octopus aorta has a larger component of muscle, and lesser amounts of collagen and e l a s t i c f i bres than are found in mammalian a r t e r i e s (Burton, 1965). These differences in tissue composition may account for the lower e l a s t i c modulus and greater hysteresis in the octopus aorta, compared to mammalian a r t e r i e s . The role of the muscle in the octopus 151 vessel wall remains uncertain at t h i s time. Clearly there must be present a c e l l u l a r component which i s responsible for the deposition of the e x t r a c e l l u l a r connective tissues. Muscle c e l l s may also provide a mechanical linkage between fibres in the e l a s t i c network (see Chapter I I ) . In addition, the muscle may contribute to active propulsion of blood through the c i r c u l a t i o n , but this has not yet been c l e a r l y demonstrated (Johansen and Martin, 1962; Wells, 1978). It seem unlikely that muscle activation in the aorta could be important in regulating blood flow resistance since t h i s parameter must be influenced predominantly by the peripheral vessels. 2. Structural Basis of Non-Linear E l a s t i c i t y The non-linear e l a s t i c properties of the mammalian artery wall are attributed to the p a r a l l e l arrangement of e l a s t i n and collagen f i b r e systems. E l a s t i n i t s e l f has non-linear e l a s t i c i t y because of i t s non-Gaussian behaviour (Aaron and Gosline, 1981). However, the increase in s t i f f n e s s of an e l a s t i n fibre with extension i s not nearly as great as the increase in s t i f f n e s s which occurs with comparable strains in the intact artery wall. Thus, the " J " shape of the s t r e s s - s t r a i n curve for the mammalian artery a r i s e s , not from the non-linear properties of e l a s t i n , but from the recruitment of more e l a s t i n fibres and the transfer of load to.the collagen network, as the artery i s i n f l a t e d (Roach and Burton, 1957; Wolinsky and Glagov, 1964). 152 In contrast, i t appears that the non-linear e l a s t i c i t y of the OAE fibres may be important in determining the shape of the st r e s s - s t r a i n curve for the octopus aorta. It was shown in Chapter IE that the OAE protein chains are more r e s t r i c t e d in their f l e x i b i l i t y than those in e l a s t i n . Consequently, the s t i f f n e s s of the OAE fi b r e s increases rapidly with stretch in the region of non-Gausian extensions. In Figure 4.18 the shapes of the s t r e s s - s t r a i n curves for the octopus artery wall and for the OAE fibres are compared. Here, the stress scales have been adjusted a r b i t r a r i l y so that the i n i t i a l portion of the curves coincide (up to 6 = 0.2). When this i s done, i t can be seen that the curves are almost i d e n t i c a l in form up to strains of 1.2. Thus, the non-Gaussian behaviour of the e l a s t i c f i bres gives r i s e to an increase in s t i f f n e s s , with extension, which i s similar to the non-linear e l a s t i c i t y of the whole artery wall, up to and including the normal range of physiological extensions. It was also shown in Chapter III that the e l a s t i c f i b r e network comprises about 3% of the volume of the aorta, and that the fibres are present as a sheet l i n i n g the vessel lumen, and as a mu l t i d i r e c t i o n a l array throughout the muscle layers. Figure 4.18 shows that up to £ = 1.2 the stress required to stretch the e l a s t i c f i bres i s about 100 times as great as the circumferential stress in the whole artery wall (i.e the stress scales in F i g . 4.18 d i f f e r by a factor of about 100). If as l i t t l e as one t h i r d of the t o t a l f i b r e content ( i . e . about 1% of the wall area), i s oriented to 153 0 .4 .8 1.2 1.6 Strain F i g u r e 4.18. Nominal s t r e s s v s . s t r a i n f o r octopus a o r t a ( c i r c u m f e r e n t i a l d i r e c t i o n ) , f o r OAE - the octopus a r t e r i a l elastomer, and f o r a Gaussian rubber with the same e l a s t i c modulus as the OAE (dotted l i n e ) . L e f t o r d i n a t e i s f o r the a o r t a ; r i g h t o r d i n a t e i s f o r the OAE and the rubber, [nominal s t r e s s = true s t r e s s / ( s t r a i n + 1 ) ] . S t r e s s s c a l e s are a d j u s t e d so that the i n i t i a l p o r t i o n of the curves c o i n c i d e (up to a s t r a i n of 0.2). 1 54 support the circumferential stress when the artery i s i n f l a t e d , then the presence of e l a s t i c f i b r e s alone can account for the s t i f f n e s s of the artery wall through the physiological range of pressures. Collagen, which is present as a loose adventitia, may not be required to take a s i g n i f i c a n t portion of the load u n t i l very large extensions. 3. The Octopus Aorta as an E l a s t i c Reservoir The octopus aorta has been shown to be a v i s c o e l a s t i c structure, in which the dynamic e l a s t i c modulus E* and the viscous damping both increase continuously with frequency, over the range of 0.05 to 10 Hz. Studies of dynamic e l a s t i c properties in mammalian a r t e r i e s have shown similar resu l t s ; with increasing frequency E* increases by 1.1 to 2 times the s t a t i c value, and tan & also increases, ranging from about 0.09 to 0.20 (Bergel, 1961b; Gow, 1970; Patel et a l . , 1973; Busse et a l . , 1981). The magnitude of the wall v i s c o s i t y in mammalian art e r i e s i s well correlated with the proportion of vascular muscle, as are hystersis and stress-relaxation (Dobrin, 1978). In terms of tan 6 and the r e l a t i v e change in E* between 0 and 10 Hz, the octopus aorta i s comparable to the c a r o t i d artery of mammals. Wall v i s c o s i t y causes attenuation of pressure waves in the aorta, which in turn may help reduce the impedance to flow which the heart must work against (Taylor, 1966a). V i s c o s i t y also dissipates energy as heat and decreases the e f f i c i e n c y of e l a s t i c energy storage in the system. Thus, the 155 amount of damping in the aorta of any animal may represent an optimum contribution to several hemodynamic variables. Resilience in the octopus aorta varies from about 70% to 60% over the physiological range of frequencies (0.1 to 1.0 Hz), or s l i g h t l y less than the r e s i l i e n c e of the mammalian aorta (Wainwright et a l . , 1976). It appears that the octopus aorta has mechanical properties which allow i t to function e f f e c t i v e l y as an e l a s t i c reservoir in the c i r c u l a t i o n . In the next chapter the mechanical properties of th i s vessel w i l l be related to some aspects of cardiovascular dynamics in the l i v i n g octopus. 156 CHAPTER V. HEMODYNAMICS OF THE OCTOPUS ARTERIAL CIRCULATION A. INTRODUCTION The relations between pressure and flow in a r t e r i a l systems are determined to a large part by the v i s c o e l a s t i c properties of the a r t e r i e s (McDonald, 1974). The d i s t e n s i b i l i t y of the artery wall i s characterised by i t s modulus of e l a s t i c i t y , and t h i s i s an important factor_ in determining the v e l o c i t y of pressure and flow waves through the system (Mirsky, 1967). In addition, these t r a v e l l i n g waves in a r t e r i e s are attenuated because some mechanical energy i s dissipated as heat by the v i s c o s i t y of the artery wall (McDonald and Gessner, 1968). Impedance to blood flow in a r t e r i e s i s also determined, in part, by the v i s c o e l a s t i c properties of the wall (McDonald, 1974). Thus, with a knowledge of the mechanical behaviour of the a r t e r i e s , i t i s possible to make quantitative predictions about wave vel o c i t y , attenuation and impedance, and these, in turn, allow one to characterise the cardiovascular dynamics in the l i v i n g animal. For steady laminar flow in a c y l i n d r i c a l tube, P o u i s e i l l e ' s Law describes the volume flow rate as being d i r e c t l y proportional to the pressure gradient and to the fourth power of radius, and inversely proportional'to the f l u i d v i s c o s i t y and the tube length. The a p p l i c a b i l i t y of t h i s relationship to closed c i r c u l a t o r y systems is severely limited for a number of reasons, the major one being that the 1 57 flow from the heart is highly p u l s a t i l e . This factor, gives ri s e to much more complicated pressure-flow relationships than predicted by P o u i s e i l l e ' s Law. Further complexities result from the v i s c o e l a s t i c i t y of the vessel wall and the presence of r e f l e c t i o n s i t e s at various points along the a r t e r i a l tree (McDonald, 1974). A simple model which can be used to describe p u l s a t i l e flow considers the a r t e r i a l system as a compliant e l a s t i c chamber or "Windkessel", which i s connected in series to a non-compliant peripheral resistance (Fig. 1A). The chamber distends with blood from the heart during s y s t o l i c ejection, and discharges blood through the resistance, by passive e l a s t i c r e c o i l during d i a s t o l e . The intermittant flow from the • heart i s transformed by the e l a s t i c i t y of the chamber into a r e l a t i v e l y steady output to the periphery. The importance of t h i s pulse smoothing effect by the large a r t e r i e s in the mammalian c i r c u l a t i o n has been recognised since the eighteenth century (see McDonald, 1974). An alternative representation of the Windkessel concept i s by the e l e c t r i c a l c i r c u i t shown in Figure 1B, in which the capacitor i s the analogue of the e l a s t i c chamber and the r e s i s t o r takes the place of the peripheral vessels (Spencer and Dennison, 1963). The Windkessel is a "lumped parameter" model because a l l of the compliance is associated with the chamber, while a l l of the resistance i s in the peripheral vessels. In other words, the major a r t e r i e s which comprise the e l a s t i c chamber 158 A B F i g u r e 5.1. A) The Windkessel model of the c i r c u l a t i o n . An e l a s t i c chamber C, r e p r e s e n t i n g the major a r t e r i e s , i s connected to a non-compliant r e s i s t a n c e (R), r e p r e s e n t i n g the p e r i p h e r a l v a s c u l a t u r e . The i n f l o w to the system (Qin) has two components: the flow s t o r e d by the chamber (Qc) and the outflow a c r o s s R (Qr). B) The e l e c t r i c a l analogue of the Windkessel model. The e l a s t i c chamber i s represented by a c a p a c i t o r (C) and the outflow r e s i s t a n c e i s represented by a r e s i s t o r (R). 1 59 offer no resistance to flow, and the peripheral resistance vessels have no e l a s t i c storage capacity. This model assumes that there i s a d i s t i n c t d i v i s i o n between capacitive and r e s i s t i v e portions of the a r t e r i a l tree (McDonald, 1974). Another inherent assumption of the Windkessel model is that pressure changes occur simultaneously throughout the system; that i s , the pressure pulse i s transmitted at i n f i n i t e veloc i t y . Although too s i m p l i s t i c in many ways to give an accurate description of some complex c i r c u l a t o r y systems, the Windkessel model i s a t t r a c t i v e as a f i r s t approach to hemodynamics because i t can be represented by simple equations. Relations between volume flow and pressure are obtained by considering the inflow, the outflow and the rate of storage. The rate of volume flow into the system, Qin, w i l l be equal to the f i l l i n g rate of the of the e l a s t i c chamber, Qc, plus the outflow through the resistance, Qr. Qr represents the "steady flow" component which, by analogy to Ohm's Law, i s equal to P/R, where P i s pressure and R i s peripheral resistance. Qc w i l l equal dV/dt, where V i s the chamber volume. The d i s t e n s i b i l i t y of the chamber i s given by the volume compliance C, which equals dV/dP. Qc can be expressed in terms of the compliance and the pressure d i f f e r e n t i a l : Qc = (dV/dP) X (dP/dt) = C(dP/dt) (5.1) Under steady state conditions, the t o t a l flow through 160 the system in each cycle may be expressed as the sum of a steady and a p u l s a t i l e component: Qin = C (dP/dt) + P/R (5.2) Qin w i l l be positive in systole and zero in di a s t o l e . While the heart r e f i l l s the chamber empties through R, with pressure following an exponential decline. The r a t i o of p u l s a t i l e pressure to p u l s a t i l e flow i s the vascular impedance (McDonald, 1974). Since flow into the Windkessel w i l l increase in proportion to the rate of o s c i l l a t i o n ( i . e . dP/dt), the impedance of the Windkessel must drop continuously with increasing frequency of pressure pulsation. In application to mammalian c i r c u l a t i o n , the major fau l t of the Windkessel model i s that i s makes no allowance for wave propagation effects which result from f i n i t e transmission times (Taylor, 1964). When a r t e r i a l pressure waves are propagated over distances which approach or exceed the wavelength, as is the case in mammals (Noordergraaf et a l . , 1979), the system does not behave l i k e an e l a s t i c reservoir. Rather, the mammalian a r t e r i a l tree i s better described by transmission l i n e theories. The a r t e r i a l pressure pulse may be considered as made up of a series of sine waves of harmonic frequencies, where the v e l o c i t y and attenuation of the component waves is frequency dependent. Higher frequencies travel farther in terms of wavelength, and ref l e c t e d waves combine in a manner 161 which gives r i s e to a variety of complex transmission e f f e c t s that are marked in the mammalian c i r c u l a t o r y systems which have been studied. These e f f e c t s include amplification and d i s t o r t i o n of the pressure pulse as i t travels peripherally, and o s c i l l a t i o n s in the impedance and apparent wave ve l o c i t y with increasing frequency. Additional complications to the transmission l i n e model of the mammalian a r t e r i a l tree are the presence of e l a s t i c taper, and d i s t r i b u t e d r e f l e c t i o n s i t e s along i t s length. The wave transmission properties of the mammalian c i r c u l a t i o n have been extensively described in a series of model studies by Taylor (I957a,b, 1959, 1964, 1965, 1966a,b). Recently, i t has been shown that a r t e r i a l hemodynamic relationships in small poikilothermic vertebrates such as t u r t l e s and frogs can be adequately described by Windkessel models (Burggren, 1977; L a n g i l l e and Jones, 1977). The important difference between these animals and mammals i s that, for comparable siz e , the resting heart rate in poikilotherms i s considerably lower. This means that the transmission time of the pressure pulse through the a r t e r i a l c i r c u l a t i o n becomes a n e g l i g i b l e proportion of the cardiac cycle, and therefore complex wave propagation theories are not necessary to model the dynamics of blood flow in these animals. Previous studies have shown that the octopus has a r e l a t i v e l y high pressure a r t e r i a l system and low heart rate (Johansen and Martin, 1962; Wells, 1979). It is possible that the t r a n s i t time of the pressure pulse through the octopus 162 a r t e r i a l tree is also a small fraction of the cardiac cycle. If t h i s i s true then the octopus c i r c u l a t i o n may be reasonably well described by a simple Windkessel. In the previous chapter i t was demonstrated that the octopus aorta i s a r e s i l i e n t e l a s t i c tube, much l i k e the a r t e r i e s of vertebrates, and i t was suggested that t h i s vessel might function as an e l a s t i c reservoir in the c i r c u l a t o r y system of the octopus. The purpose of th i s study is to analyse the aorti c pressure and flow relationships in the aorta of 0. d o f l e i n i by in vivo measurements and, with a knowledge of the mechanical properties of the artery wall, to test the v a l i d i t y of the Windkessel as a model of blood c i r c u l a t i o n in the octopus. 1 63 B. METHODS 1. Measurements of Aortic Blood Pressure and Flow The experiments were performed on fi v e healthy specimens of 0. d o f l e i n i weighing from 8 to 11 kg. The animals were anaesthetised by c h i l l i n g (see chapter IV), or by addition of ethanol to 2% in the sea water (Johansen & Martin, 1962; Wells, 1979). During this time respiratory movements generally ceased. The surgical procedure involved cannulation of the systemic aorta and implantation of a blood flow probe on thi s vessel. A mid-line i n c i s i o n was made through the dorsal mantle wall, several cm anterior to the heart (see F i g . 1.1). The aorta was exposed afte r c a r e f u l l y opening the underlying body wall. In thi s region there are no branch vessels on the aorta; for cannulation the vessel was clamped, sectioned and rejoined via a short v i n y l T piece (Fig. 5.2). The T piece was located about 5 cm from the heart. This operation usually took 10-15 minutes, and blood loss appeared to be very s l i g h t . In each case, the diameter of the T piece was selected to match approximately the anticipated aor t i c diameter for resting d i a s t o l e . Two i d e n t i c a l lengths of PE 90 tubing were inserted into the T piece, and one was advanced a measured distance toward the heart after the vessel was undamped. The catheters were f i l l e d with sea water and connected to Bio-tec BT 70 pressure transducers. In addition, the T piece contained a flow probe which was connected to a Biotronix BL 164 to pressure transducer Vinyl T J to flowmeter Flow Probe F i g u r e 5.2. The T-peice cannula f o r the a o r t a . The flow probe was attached adjacent to the v i n y l T. Pressure c a t h e t e r tubes were fed through the T i n t o the a o r t a . 165 610 electromagnetic flowmeter, and a pneumatic flow occluder, which was used to es t a b l i s h zero flow. Immediately after surgery, the animal was revived in an aquarium f i l l e d with aerated sea water at 8-10 degrees C. Providing that the sensitive outer skin was not stitched, the animals seemed not to be i r r i t a t e d by the presence of the T tube. Recording sessions were successfully c a r r i e d out over periods of several hours on unrestrained, unansthetized animals. In order to achieve reasonable measurements of the "resting" state, the animals were maintained undisturbed under low l i g h t l e v e l s in covered aquaria. Pressure transducers were calibrated s t a t i c a l l y against a column of sea water, and dynamically by monitoring the free vibrations from a pressure transient applied at the catheter t i p s ("pop" test, Gabe, 1972). The resonant frequency of the pressure recording system was t y p i c a l l y over 40 Hz and, since th i s i s about 40 times greater than the highest frequencies recorded in these experiments, no corrections to the pressure signals were necessary. The electromagnetic flow meter was calibr a t e d for volume flow rate (ml/sec) by perfusing the flow probe on the T tube with saline. Volume flow rates were measured by timing the c o l l e c t i o n of known amounts of perfusate, and these rates were compared with the analogue output from the flowmeter. The zero flow c a l i b r a t i o n obtained by occlusion was confirmed later in the experiment by in j e c t i o n of acetylcholine. This caused the heart to slow to less than 5 beats per minute and, 166 at these low heart rates a constant l e v e l of flow at the end of diastole was assumed to be true zero. Dynamic c a l i b r a t i o n was not performed, but a previous study using the same flowmeter (Langille & Jones, 1977) showed that signal d i s t o r t i o n would be neg l i g i b l e at the low frequencies encountered in this investigation. Pressure and flow data were recorded on an instrumentation FM tape recorder (Hewlett-Packard 3907C) and displayed simultaneously on a s t r i p chart recorder (Gulton Techni-rite TR888) or played back from the tape onto a Hewlett-Packard pen recorder (HP-7402A). 2. Determination of the Input Impedance Tracings of pressure and flow pulses (5 to 20) were d i g i t i s e d and averaged to improve the signal to noise r a t i o using an analogue-to-digital converter and a Mine 11/03 computer ( D i g i t a l Equipment Corp.). A sampling i n t e r v a l of 0.08'seconds allowed each pulse to be described by about 75 points. These data were then subjected to a Fourier analysis for determination of the aort i c impedance spectrum as follows. Assuming that the c i r c u l a t o r y system is in a steady state during a given time i n t e r v a l , then pressure (P) and flow (Q) o s c i l l a t i o n s during that i n t e r v a l can be represented as periodic functions by f i n i t e Fourier (harmonic) series. Thus, 167 iV P(t) * Po + _£ [An cos(nwt) + Bn sin(nwt)] (5.3) where P(t) i s the pressure function, Po i s the s t a t i c or mean pressure (the zero frequency value), An and Bn are the Fourier c o e f f i c i e n t s , n i s the harmonic number, N is the t o t a l number of harmonics (N=9 in t h i s study), and w = 2 f r f , where f i s the fundamental frequency ( i . e . , the reciprocal of the the period of the heartbeat, T). The function Q(t) i s s i m i l a r l y represented. To solve for the mean value Po and the c o e f f i c i e n t s An, Bn are determined by f i n i t e summations (Attinger et a l . , 1966; Gessner, 1972): Ao = 1/K ^ P ( x A t ) (5.4) An = 2/K ^ P ( x A t ) cos(21Tnx/K) (5.5) X - O Bn = 2/K P ( x A t ) sin(2 tr nx/K) (5.6) x = c> where dt i s the sampling i n t e r v a l , K i s the number of samplings obtained and K A t = T, the period of the heartbeat. Thus, the A/D conversion replaces the continuous function P(t) with a discrete set of K values, P ( x A t ) . The sine and cosine terms for each harmonic may be combined so that equation 5.3 is rewritten in terms of a modulus (Pn) and a phase angle (<Xn): N P(t) ^ Po + £ Pn cos(nwt - -Xn) (5.7) Pn, and o<n are calculated from An and Bn according to the trigonometric relationships: Pn a = An z + Bn a (5.8) 168 (X n = tan"' Bn/ An (5.9) By s i m i l a r i t y to equation 5.5, the blood flow function Q(t) i s written as N, Q ( t ) ^ Qo + ^ Qn cos(nwt - £n) (5.10) Vascular resistance (R) can be calculated from the ra t i o of mean a r t e r i a l pressure to mean a r t e r i a l flow, R = Po/Qo (5.11) The vascular input impedance, Z, i s defined as the ra t i o of o s c i l l a t o r y pressure to o s c i l l a t o r y flow, and expresses the "dynamic resistance". Z i s computed from the sinusoidal pressure and flow components at each frequency, as determined by the Fourier analysis. Since each harmonic term is expressed in modulus and phase form, we have impedance modulus (Z) and phase (c/>) , def ined as: Zn = Pn/Qn (5.12) c6n = ( p n - <*n) (5.13) In the absence of re f l e c t e d waves at the o r i g i n , the input impedance would be equivalent to the c h a r a c t e r i s t i c impedance (Zo) for the hydraulic system. Zo i s related to the compliance of the e l a s t i c tube, and can be calculated by the following r e l a t i o n (Gessner, 1972): Zo = p Co/ 1 T r ^ (5.14) where Co i s the c h a r a c t e r i s t i c or true pressure wave ve l o c i t y 169 (see equation 5.18), r i s the internal radius and ^ i s the f l u i d density ( ca. 1.03 g/cm^). 3. Theoretical Determination of the Input Impedance A theoret i c a l input impedance spectrum was calculated for the octopus c i r c u l a t i o n , based on the e l e c t r i c a l analogue of the Windkessel model shown in Figure 5.1B. Impedance modulus and phase are calculated as: /Z/(f) = R/[ } + {2^tT)a]^ (5.15) 0(f) = -tan"' (21T fT) (5.16) where R i s the vascular resistance (equation 5.11),. f i s the frequency and T i s the time constant of the Windkessel (Langille and Jones, 1977). In t h i s model d i a s t o l i c pressure f a l l s exponentially with time, and T can be estimated from experimental data as: T = t/ln(Pi/Pt) = RC (5.17) where t i s the length of the d i a s t o l i c period, Pi and Pt are, respectively, the pressures at the beginning and end of d i a s t o l e . C is the capacitance of the system. For a given pressure pulse, the flow terms Qin, Qc and Qr could be predicted from equation 5.2, by using values of R and C computed from equations 5.11 and 5.17. 4 . Determination of Pressure Wave Velocity in the Aorta Pressure wave ve l o c i t y was determined in three 170 d i f f e r e n t ways. F i r s t , pulse wave ve l o c i t y was estimated by measuring the t r a n s i t time of a pressure pulse along a given length of aorta. To do t h i s , pressure recordings made simultaneously at two d i f f e r e n t locations were d i f f e r e n t i a t e d (using a Biotronix BL620 analogue computer) and the resultant dP/dt signals were compared for an estimate of the t r a n s i t time. Secondly, the c h a r a c t e r i s t i c v e l o c i t y of a x i a l pressure waves in a thick-walled e l a s t i c tube, Co, may be calculated from: Co = (2E'h/3 -o r)Vx (5.18) where E' is the dynamic e l a s t i c (storage) modulus of the wall in the circumferential d i r e c t i o n , and h i s the vessel wall thickness (Mirsky, 1973; Saito and VanderWerf, 1975). Thirdly, in v i t r o experiments were designed to measure the v e l o c i t y of sinusoidal pressure waves in the octopus aorta over a wider range of frequencies than occurs in vivo. To do t h i s , an almost complete aorta (about 16 cm in length) was dissected from an octopus under anaesthesia. The artery was cannulated and mounted in the tissue bath of the i n f l a t i o n apparatus as shown in Figure 5.3. Steady perfusion of the vessel was provided by a saline reservoir, which was pressurized to 0.6 atmospheres (600 cm of water) above the ambient pressure by a compressed a i r source. Flow from this chamber was regulated so that a large pressure drop occured across the needle valve at the inflow to the pump, while only 171 Pulse Wave Velocity in vitro A P *\j RH V Transfer Funct ion Analyser • Amplitude •Phase C = L 2 TT f e F i g u r e 5.3. The apparatus f o r measuring pressure wave v e l o c i t y i n the a o r t a i n v i t r o . P1 and P2 aire the pre s s u r e s measured at the i n f l o w (proximal) and outflow ( d i s t a l ) s i t e s r e s p e c t i v e l y . C i s apparent v e l o c i t y , L i s the d i s t a n c e between P1 and P2, f i s frequency and 0 i s the phase s h i f t between P1 and P2 s i g n a l s . 172 a small pressure drop occurred across the valve at the outflow of the vessel segment. This arrangement allowed perfusion of the artery at a constant pressure (30 and 60 cm of water were used), and prevented o s c i l l a t o r y flow from the pump from passing back into the reservoir (see Caro and McDonald, 1961). The diaphragm pump was driven by an electromagnetic vibrator, and t h i s was used to impose small sinusoidal volume changes on the i n f l a t e d artery such that the resulting pressure o s c i l l a t i o n s were no more than 3 cm of water peak-to-peak. Under these conditions the pressure waves were e s s e n t i a l l y sunusoidal. Simultaneous measurements of the proximal and d i s t a l pressures, P1 and P2 respectively, were made with two id e n t i c a l BioTec BT-70 pressure transducers. These signals were amplified through matched D.C. amplifiers (SE Labs, Type 4200). The amplitude and phase of the two pressure waves were measured at each frequency by a transfer function analyser (SE Labs, type SM272DP) as described by Denny and Gosline (1980). The pressure transducers were calibr a t e d as described in section (1) above. Apparent pulse wave v e l o c i t y , C was computed as a function of frequency by the r e l a t i o n : C = 2if fL / d e (5.19) where f i s the frequency, de i s the phase difference in radians between P1 and P2, and L is the distance between the measuring s i t e s in the artery segment. At zero pressure L was 1 73 11.4 cm, but L increased to 12.0 and 13.7 cm at pressures of 30 and 60 cm of water respectively. These changes occurred because the aorta lengthened with increased pressure (see Chapter IV). Transmission ra t i o s were calculated as the amplitude of the o s c i l l a t i o n at the d i s t a l s i t e divided by i t s amplitude at the o r i g i n ( i . e . P2/P1). Transmission per wavelength in a uniform v i s c o e l a s t i c tube (neglecting f l u i d v i s c o s i t y ) i s given as exp( - fr tan <S ), where tan 6 i s the loss tangent of the wall (Tay.lor, 1966a). This relationship was used to predict wave transmission r a t i o s in the artery segment. 174 C. RESULTS 1. Aortic Blood Pressure and Flow in the Resting Octopus With few exceptions, the systemic heart rate in resting animals at 8 to 10 degrees C ranged from 8.5 to 14 beats per minute ( i . e . , 0.14 to 0.23 Hz), while aort i c blood pressure varied from 21 to 29 cm of water at end diastole and from 36 to 61 cm of water at peak systole. Occasionally however, during periods of spontaneous movement or s l i g h t disturbance, blood pressures as high as .45 cm of water d i a s t o l i c and 80 cm of water s y s t o l i c were recorded. These values for heart rate and blood pressure are in agreement with those reported previously for thi s species (Johansen and Huston, 1962; Johansen and Martin, 1962; Johansen, 1965). Aortic blood flow rate reached peak le v e l s which varied with pressure but was usually within the range of 1.4 to 2.8 ml/sec. These values correspond to flow v e l o c i t i e s , averaged across the vessel lumen, of approximately 10 to 24 cm/sec. A t y p i c a l example of analogue pressure and flow records is shown in Figure 5.4. D i g i t i z e d , signal-averaged pressure and flow data from Figure 5.4 are plotted in Figure 5.5. The shape of these waveforms indicates the presence of a central e l a s t i c reservoir. S y s t o l i c ejection begins with a rapid r i s e in both the pressure and the flow v e l o c i t y . Peak flow i s reached after about one second, while peak pressure is attained some 600 milliseconds l a t e r . The end of systole i s not marked by an incisura in the pressure wave or by flow 175 50, O CM E o 0 L blood pressure -i50 blood flow ] 20 sec 5 sec F i g u r e 5.4. Analogue p r e s s u r e and flow recorded i n the a o r t a of the r e s t i n g octopus. 1 7 6 ^ 5 0 r x E , 0 , 3 tn 25' I I I 1 1 - L -0 1 2 3 4 5 seconds F i g u r e 5 . 5 . D i g i t i z e d s i g n a l averaged p r e s s u r e and flow curves from the data i n F i g u r e 5 . 4 . 1 77 r e v e r s a l as i t i s i n the mammalian a o r t a . However, cl o s u r e of the a o r t i c valves and the beginning of d i a s t o l e presumably occurs at the point of i n f l e c t i o n i n the decreasing flow curve, which comes about 1.5 seconds a f t e r i t s peak value. A corresponding change i n slope i s l e s s d i s t i n c t in the pressure curve. Both flow and pressure continue to decrease a s y m p t o t i c a l l y towards the e n d - d i a s t o l i c values, which for flow i s approximately zero. The slow decay i n pressure, and the sustained p o s i t i v e flow of blood through the aorta while the heart r e f i l l s i n d i c a t e s that the a r t e r y w a l l i s r e l e a s i n g energy stored e l a s t i c a l l y during s y s t o l i c d i s t e n s i o n , thereby maintaining d i a s t o l i c flow to the p e r i p h e r a l v e s s e l s . 2. A o r t i c Impedance Spectra The frequency dependent r e l a t i o n s h i p s between pressure and flow waveforms can be q u a n t i f i e d i n terms of the r e l a t i v e amplitudes and phase angles of t h e i r r e s p e c t i v e harmonic components. Fou r i e r a n a l y s i s allows t r a n s l a t i o n of pressure and flow waves i n t o the frequency domain. In t h i s study, f o u r i e r a n a l y s i s was performed on s i g n a l averaged data, i n order to deal with the s l i g h t v a r i a t i o n s which occurred w i t h i n a t r a i n of pulses. For example, Figure 5.5 shows the d i g i t i z e d average waveforms which have been d e r i v e d from the pressure and flow pulses i n Figure 5.4A. The amplitudes of the f i r s t s i x harmonics of the pressure and flow wave p l o t t e d i n Figure 5.5 are shown i n Figure 5.6. The zero harmonic gives the mean values of 1 78 pressure and flow ( i . e . , Po and Qo), which in t h i s case were 38.8 cm of water ( = 3.8 x 10 dynes/cm ) and 0.85 ml/sec, respectively. The modulus of the f i r s t harmonic i s the amplitude of the Fourier component at the fundamental frequency (0.18 Hz in t h i s example), while the moduli of subsequent harmonics are the Fourier amplitudes which occur at integer multiples of t h i s frequency. As would be expected from the f a i r l y smooth shape of the pressure and flow curves, the higher frequencies are r e l a t i v e l y unimportant. Ty p i c a l l y , the amplitudes of harmonics above the f i f t h were less than 5% of the amplitude of the fundamental. In addition, over 99% of the p u l s a t i l e hydraulic power (computed from pressure and flow curves, according to Gessner, 1972)' i s delivered in the f i r s t f i v e harmonics. Thus the pressure and flow pulses in the octopus aorta can be adequately described by Fourier series of five harmonics. Aortic impedence spectra for three octopuses are shown in Figure 5.7. Impedance modulus, /Z/, i s computed as the r a t i o of the amplitudes of corresponding pressure and flow harmonics (equation 5.12) and <f> i s the phase s h i f t measured between pressure and flow o s c i l l a t i o n s at each frequency (equation 5.13). For comparisons among individual animals, /Z/ i s normalized by dividing by the zero frequency impedance ( i . e . , the peripheral resistance, R). In t h i s way, the r e l a t i o n between the resistance to steady and p u l s a t i l e flows is emphasized. In a l l animals, impedance modulus decreased sharply from the i n i t i a l value at zero frequency to 179 " pressure • flow 1 2 Harmonic Figure 5.6. Modulus (=amplitude) of the f i r s t six harmonics of pressure and flow for the curves shown i n Figure 5.5. The fundamental frequency i s the f i r s t harmonic, which was 0.18 Hz i n t h i s example. The mean value of each function i s given by the zero harmonic. 180 1.0i .8 F i g u r e 5.7. A o r t i c impedance s p e c t r a f o r three octopuses. Data represent a t o t a l of 150 s i g n a l averaged p u l s e s of pressure and of flow, and are shown f o r the f i r s t f i v e harmonics. Impedance modulus /Z/, i s normalized by the zero frequency r e s i s t a n c e R. Normalized c h a r a c t e r i s t i c impedance (Zo) i s a l s o shown. The a c t u a l v a l u e s of R i n these experiments were 56502, 45012 and 77713 dyne sec/cm s , while Zo/R ranged from 0.023 to 0.028. Negative phase angles i n d i c a t e that flow l e a d s p r e s s u r e . 181 approximately 20% of t h i s at the f i r s t harmonic. At frequencies above the fundamental, the impedance displayed a general but much more gradual decline to around 10% of the peripheral resistance. The c h a r a c t e r i s t i c impedance, Zo, was calculated for each aorta by using equation 12 and 13, with data for the modulus of e l a s t i c i t y taken from Chapter IV. The average value of Zo/R was 0.026, and this i s indicated by the dashed l i n e in Figure 5.7. Impedance phase was always negative (flow leading pressure), decreasing to about -0.65 radians (-37 degrees) at the f i r s t harmonic, and fluctuating somewhat around th i s value at higher harmonics. The impedance curves for the octopus aorta are substantially d i f f e r e n t from the curves which describe the input impedance of large a r t e r i e s in mammals such as rabbits, dogs and man. In mammals the a o r t i c impedance modulus drops rapidly from the zero frequency value, and o s c i l l a t e s above and below the c h a r a c t e r i s t i c impedance for the vessel, eventually s e t t l i n g at about the l e v e l of Zo after 4 or 5 harmonics (O'Rourke & Taylor, 1967; McDonald, 1974; Cox & Pace, 1975; Milnor, 1982) just as predicted for a non-uniform transmission l i n e (Taylor, 1964, 1965, 1966a). Impedance phase in the mammalian aorta shows large negative values i n i t i a l l y , but t y p i c a l l y increases to zero at the frequency of the minimum in modulus; thereafter, impedance phase may become posit i v e but f i n a l l y l e v e l s off at about zero at the higher harmonics. Since Zo defines the pressure/flow r a t i o in the complete absence of r e f l e c t e d waves, the mammalian aorta 182 operates e s s e n t i a l l y as a r e f l e c t i o n - f r e e system at frequencies above the second or t h i r d harmonic (Taylor, 1964, 1966a). In mammals, only the low frequency components of the a o r t i c impedance spectrum, where modulus ris e s above the l e v e l of the c h a r a c t e r i s t i c impedance and phase i s negative, are dominated by strong wave re f l e c t i o n s (Taylor, 1966a; Milnor, 1975; Noordergraaf, 1978). No large o s c i l l a t i o n s in either modulus or phase are evident in the octopus a o r t i c impedance spectrum. However, impedance modulus does show a continual decline with increasing frequency, but remains 2.5 to 5 times greater than the predicted r e f l e c t i o n - f r e e impedance, Zo, after 5 or 6 harmonics (Figure 5.7). Thus, i t appears that the major harmonics of the pressure and flow pulse in the octopus aorta a l l occur at low frequencies where wavelengths are r e l a t i v e l y long with respect to the length of the a r t e r i a l tree. Therefore, a l l waves which are refected from peripheral s i t e s should reach the heart without s i g n i f i c a n t attenuation or phase s h i f t , and consequently the aorta should behave e s s e n t i a l l y as a single e l a s t i c reservoir (Noordergraaf, 1978). Accordingly, complex transmission l i n e models should not be necessary to describe pressure and flow relationships in the octopus aorta. Instead we expect that a simple Windkessel model w i l l adequately describe the c i r c u l a t i o n in t h i s cephalopod. 183 3. Application of the Windkessel Model In Figure 5.8, impedance data are plotted for one octopus, along with modulus and phase curves predicted for that animal from the e l e c t r i c a l analogue of the Windkessel model (equations 5.15 and 5.16). This simple two-element model gave a reasonable approximation of the impedance data, p a r t i c u l a r l y at the lower frequencies, although the predicted values of modulus and" phase were consistently s l i g h t l y lower than those observed. In r e p t i l i a n and amphibian c i r c u l a t i o n s which have been modelled by a Windkessel, similar deviations from the predicted impedance modulus and phase have also been observed (Burggren, 1977; L a n g i l l e & Jones, 1977). The differences between measured and predicted aor t i c impedance in the octopus l i k e l y a r i s e , for the most, part, because in a l l cases the flow probe was positioned a few centimeters from the heart (this was due to surgical d i f f i c u l t y in reaching the aort i c root without rupturing large venous sinuses). The flow measurements were made, not at the outflow from the v e n t r i c l e , nor at the peripheral resistance, but from within the e l a s t i c reservoir. Therefore, the data presented in Figures 5.7 and 5.8 do not t r u l y represent the input impedance of the entire aortic Windkessel, as do the model curves; rather, these measured values describe the l o c a l f l u i d impedance; that i s , the input impedance to that portion of the a r t e r i a l c i r c u l a t i o n which is d i s t a l to the probe. The impedance spectrum must surely be altered along the length of the aorta, as the p u l s a t i l e 184 Figure 5.8. Impedance data for one octopus, compared to model curves predicted from the Windkessel model in Figure 5.1B (equations 5.15 and 5.16). 185 inflow from the heart i s transformed to a much smoother flow by the compliance of the vessel. Figure 5.9 i l l u s t r a t e s this point. Here, based on the records of pressure and flow shown in figure 5.5, the components of flow through the Windkessel model have been calculated, according to equation 5.2. In thi s example, Po = 39.5 cm of water (3.87 x 104" dynes/cm 2), Qs = 0.885 ml/sec, R = 44.6 cm of water (4.37 x 10 4 dyne sec/cm5") , T = 5.99 seconds, C = 0.13 ml/cm of water (1.37 x 10 4 cm^/dyne). The calculated outflow through the peripheral resistance Qr, appears r e l a t i v e l y steady and i s in phase with pressure. On the other hand, the calculated flow which i s stored in the reservoir Qc, is highly p u l s a t i l e and i s in phase with the pressure d i f f e r e n t i a l ; that i s , the harmonics of Qc lead those of pressure by 90 degrees. Qc i s positive when the reservoir i s charging and negative when i t is discharging, the mean value of Qc being zero under steady state conditions. Qin, the sum of Qc and Qr, i s the t o t a l flow into the system which, as expected, is large in systole and f a l l s to zero during d i a s t o l e . The change in the shape of the flow pulse (from Qin to Qr) as flow passes through the highly compliant aorta, involves a reduction in the pulse amplitude and a phase s h i f t in the harmonic flow components of almost 90 degrees with respect to the pressure pulse. The actual flow pulse which was measured part way along the aorta, Q(t), appears to have p a r t i a l l y undergone this transformation. The sustained d i a s t o l i c flow seen in Q(t) must be supplied by 186 Figure 5.9. Components of flow through Windkessel model predicted from pressure pulse P(t) which was measured in the octopus. Qr is the outflow across the r e s i s t o r and varies with P. Qc i s the flow into or out of the chamber and varies as dP/dt. Qin is the t o t a l flow into the system and i s the sum of Qr and Qc. Q(t) i s the observed flow pulse corresponding to P ( t ) . 187 188 e l a s t i c r e c o i l in the upstream portion of the Windkessel,. It i s now possible to appreciate that the impedance data in Figure 5.8 should necessarily deviate from the predicted input impedance. According to the model in Figure 5.9, i f the s i t e of reference was moved from the heart towards the periphery, impedance phase would become less negative, and impedance modulus would increase. If pressure and flow were measured at the very end of the Windkessel, impedance modulus would equal R and phase would be zero. Although the choice of flow measurement sit e s may explain most of the differences between the impedance data and the Windkessel curves, some other mechanical factors undoubtedly are involved. The octopus artery wall has non-linear v i s c o e l a s t i c properties (see Chapter IV); thus, the capacitance of the aorta (C) i s not constant, but decreases as pressure r i s e s , "and the pressure decay during diastole does not f i t exactly a single exponential ( i t i s more precisely defined by a spectrum of time constants). In addition, the model assumes that a l l resistance is lumped as a single peripheral element. Thus the input impedance of a pure Windkessel tends to zero at high frequencies, and the phase tends to negative 90 degrees. In r e a l i t y , there must be some resistance to flow associated with the aorta i t s e l f and this is defined by Zo, the c h a r a c t e r i s t i c impedance (Figure 5.7 ). Zo is inversely related to the e l a s t i c modulus of the vessel wall. In the highly d i s t e n s i b l e octopus aorta, Zo is only 2% to 3% of R; nevertheless, i t s presence in the 189 Windkessel sets the minimum value which the impedance modulus may approach at high frequencies, and causes the phase to be less negative at a l l frequencies (Westerhof et a l . , 1971). Despite these inherent physical l i m i t a t i o n s , the impedance data support the Windkessel hypothesis, that the octopus a r t e r i a l tree functions e s s e n t i a l l y as a central e l a s t i c reservoir which discharges blood through a single peripheral resistance. 4. Pressure Wave Propagation in the Aorta A fundamental assumption of the Windkessel model i s that pressure changes occur at a l l points in the e l a s t i c reservoir simultaneously; that i s , the t r a n s i t time of the pressure pulse must be a n e g l i g i b l e portion of the cardiac cycle (in the ideal case, the wave ve l o c i t y i s i n f i n i t e ) . Estimates of true pressure wave vel o c i t y , Co, were obtained from equation 5.18, using values of the storage modulus, E', that were determined previously (Fig. 4.17). Table 5.1 shows that Co i s highly dependent on pressure, and to a lesser degree on frequency, due to the non-linear e l a s t i c properties of the aorta. In a 10 kg octopus, the aorta extends about 15 cm from the heart to the s i t e of arborization in the head region. For an animal with mean blood pressure of 30 cm of water a pressure pulse with fundamental frequency of 0.2 Hz should t r a v e l at about 2.25 m/sec and have a t r a n s i t time through the aorta of about 70 milliseconds. At a mean pressure of 60 cm of water the v e l o c i t y of the fundamental 190 Table 5.1 Predicted pressure wave v e l o c i t y C 0 and wavelength for two level s of mean pressure. C 0 i s calculated by equation 5.18 X i s calculated by C 0 = fX, where f i s frequency. Pressure Frequency (Hz) cm H 20 0.01 0.50 1.0 5.0 10.0 30 (m/sec) X (m) 2.17 2.31 2.34 2.46 2.54 21.7 4.02 2.34 0.49 0.25 60 C 0 (m/sec) X (m) 5.98 6.28 6.68 7.95 8.18 59.8 12.6 6.70 1.59 0.82 191 would be just over 6 m/sec, and the pulse would reach the periphery from the heart in only 25 milliseconds. Generally, mean blood pressure in the resting octopus was between 30 and 60 cm of water and so pressure transmission through the aorta should normally take a negli g i b l e portion (0.4% to 1.6%) of the cardiac cycle. Table 5.1 also gives wavelengths calculated for each frequency and pressure. Only at frequencies which are well above those of physiological importance (>5 Hz) does the length of the aorta represent an appreciable fraction of the pressure wavelength. On the basis of these calculations i t appears that, because of low heart rates, the Windkessel assumption of simultaneous pressurization of the reservoir i s v a l i d for the a r t e r i a l c i r c u l a t i o n of.O. d o f l e i n i . Next, i t was of interest to make measurements of pressure wave vel o c i t y in vivo, for comparison to the derived values of Co. Figure 5.1 OA shows a t y p i c a l example of a pressure wave in the octopus aorta which was recorded simultaneously at two si t e s 10 cm apart. The fundamental frequency was 0.13 Hz and the mean pressure was approximately 30 cm of water. The pressure pulse was transmitted through the aorta with v i r t u a l l y no change in i t s shape, and with a small degree of attenuation. Wave transmission phenomena, which cause d i s t o r t i o n and amplification of the pressure pulse in mammals, do not appear to be important in the octopus a r t e r i a l c i r c u l a t i o n . Measurements of the in vivo pressure wave velocity 192 I 2 sec i i 2 sec Figure 5.10. A) A pressure pulse i n the octopus aorta measured simultaneously at two points separated by 10 cm. (upper trace i s from the proximal s i t e ; lower trace i s from the d i s t a l site).The waves appear to be i n v i r t u a l synchrony. B) The d i f f e r e n t i a t e d pressure pulses of (A). These wave forms have a more d i s t i n c t "foot". Time differences between pairs of d i f f e r e n t i a t e d pressure waves were determined to be less than 10 milliseconds, which indicates a wave v e l o c i t y of greater than 10 m/sec. 1 9 3 proved d i f f i c u l t to make. In a l l instances, the pulse appeared at both recording s i t e s in v i r t u a l synchrony. Normally the wave vel o c i t y i s determined from the t r a n s i t time of the wave "foot" over a given distance. For the example shown in Figure 5.1 OA, t h i s was predicted from Co to be about 50 milliseconds, but no actual time difference could be discerned between the two recordings. The procedure was hindered by the fact that at high chart speeds, the wave was too rounded for the location of the foot to be precisely i d e n t i f i e d . D i f f e r e n t i a t e d pressure waves had a more sharply defined foot, and a d i s t i n c t peak (Fig. 5.10B). By comparing these waveforms the t r a n s i t time was determined to be less than 10 msec. Therefore the apparent wave ve l o c i t y was in excess of 10 m/sec, or more than four times greater than predicted for the same mean pressure. Similar large values of wave v e l o c i t y were obtained when pairs of pressure waves were subjected to Fourier analysis and the phase s h i f t s used to determine tr a n s i t times. Unfortunately, t h i s method did hot give consistent r e s u l t s , probably because the phase differences being measured were small (<1 degree), and close to the l i m i t s of resolution of the Fourier technique. The results of these determinations indicate that in vivo, the pressure wave ve l o c i t y is much higher than predicted from the mechanical properties of the artery wall. It should be noted however, that Co i s defined as the c h a r a c t e r i s t i c or true pressure wave ve l o c i t y for the tube, which l i k e the c h a r a c t e r i s t i c impedance, i s only attained in 1 94 the absence of reflected waves. Many studies on mammalian c i r c u l a t i o n s (Caro & McDonald, 1961: Bargainer, 1967; Cox, 1971; McDonald, 1974) as well as models of transmission l i n e s (Taylor, 1957b, 1966a, 1966b; Hardung, 1962; L i et a l . , 1980) have shown that only the high frequency components of the pressure pulse ( i . e . , the short wavelengths) are s u f f i c i e n t l y damped that they appear to travel at v e l o c i t i e s close to Co, just as only the high frequencies of the impedance modulus approximates to Zo. At low frequencies where wavelengths are several times longer than the artery (below the second harmonic in mammals), and damping i s s l i g h t , the apparent v e l o c i t y becomes anomalously high due to the presence of strong r e f l e c t i o n s from the periphery (Taylor, 1966a, 1966b; Noordergraaf, 1969, 1978). Measurements of foot-to-foot v e l o c i t y of the mammalian pressure pulse give close estimates of Co, only because i t i s the high frequency components which define the wave foot (McDonald, 1974). However, in the octopus even the higher harmonics of the pressure pulse (the 5th harmonic occurs at about 1 Hz) have wavelengths which are many times longer than the aorta (Table 5.1). It i s l i k e l y , therefore, that a l l s i g n i f i c a n t harmonic components in the octopus pressure pulse w i l l appear to t r a v e l at v e l o c i t i e s which are much higher than Co. If so, then i t should not be possible to obtain the true wave ve l o c i t y from the in vivo pressure pulse in 0. d o f l e i n i , and t h i s could explain why the measured values in t h i s study were so much higher than at 195 f i r s t anticipated. 5. Pressure Wave Velocity Measurements in v i t r o In order to obtain confirmation of the calculated values of Co for the octopus aorta, i t was necessary to study the propagation of pressure pulses at much higher frequencies than normally occur in the animal. Figure 5.11A shows the results of in v i t r o experiments in which small sinusoidal pressure waves were generated in a long segment of aorta which was perfused at a mean pressure of 30 cm of water The apparent pressure wave ve l o c i t y , C (calculated from eqn. 5.19), was found to be highly frequency dependent. Values of C f e l l sharply from about 30 m/sec at frequencies below 1 Hz, to a minimum of 2.30 m/sec at 6 Hz, and thereafter rose only s l i g h t l y to 2.90 m/sec at 10 Hz. Recall that Co was predicted to be approximately 2.50 m/sec at 5 to 10 Hz (Table 5.1), while C in vivo was greater than 10 m/sec at frequencies below 1 Hz. Thus, the ve l o c i t y data in Figure 5.11A are consistent with the in vivo measurements at low frequencies and with the predictions of Co at high frequencies. The results of the ve l o c i t y measurements suggest that pressure waves at frequencies above 6 Hz were propagated with l i t t l e influence from terminally r e f l e c t e d waves, while below th i s frequency r e f l e c t i o n s became increasingly important and gave r i s e to very high apparent v e l o c i t i e s . In a v i s c o e l a s t i c tube, such as an artery, a t r a v e l l i n g pressure wave w i l l be attenuated due to energy losses through 196 Jr i- 1 1 1 1 l_ I • • I i • I | 0 2 A 6 8 10 0 2 A 6 8 10 12 U 16 Frequency (Hz) m - o F i 9 V r e 5 - 1 1 - Apparent v e l o c i t y and t r a n s m i s s i o n r a t i o s measured i n v i t r o at mean pr e s s u r e s of 30 (A) and 60 (B) cm of Isee^tex^lord^ilsr 551011 *' ^  *Y ^  b ^ l i n e s 197 wall v i s c o s i t y (Taylor, 1966a) and the degree of attenuation should increase with frequency. In Figure 5.11A the transmission r a t i o i s predicted for the octopus aorta, based on the wall v i s c o s i t y measured previously (Chapter IV). However, instead of attenuation, the pressure wave was amplified d i s t a l l y , and t h i s suggests that wave r e f l e c t i o n s were present. Transmission ratios increased from 1.0 at the lowest frequency to a maximum at 5 to 6 Hz, and then decreased towards 1.0 again at the highest frequencies. These results suggest that a p a r t i a l resonance occurred in t h i s specimen at approximately the same frequency as the minimum apparent wave v e l o c i t y . When the same artery was tested at 60 cm of water (Figure 5.11B) the apparent v e l o c i t y f e l l with increasing frequency from i n i t i a l values near 100 m/sec to below 10 m/sec at 15 Hz. Transmission ratios rose continuously from 1.0 with frequency, as was seen at the lower pressure. Data for the storage modulus E', which are used to predict Co, are available only up to 10 Hz. At t h i s frequency a value of 8.18 m/sec i s obtained for Co (Table 5.1), and t h i s i s well below the apparent velocity C . The range of frequencies was not great enough to reveal a minimum in the C curve, nor a maximum in the transmission r a t i o , as were seen at the lower pressure (Fig. 5.11A). However, extrapolation of the E' data yi e l d s an estimate of C of 8.4 m/sec at 15 Hz, and t h i s i s approximately equal to the measured values of C at t h i s frequency. This suggests that the frequency of resonance at a 198 pressure of 60 cm of water may occur at close to 15 Hz. The results of these experiments show that at frequencies in the physiological range (< 1 Hz) the apparent pulse wave ve l o c i t y w i l l give no indication of the true wave vel o c i t y in the aorta. The marked deviation in C from Co at low frequencies and the apparent amplification of the t r a v e l l i n g pressure wave can be attributed to r e f l e c t i o n e f f e c t s . Only in the absence of refl e c t e d waves is the apparent v e l o c i t y determined by the v i s c o e l a s t i c properties of the tube alone (McDonald, 1974). 199 D. DISCUSSION 1 . Pressure and Flow Waveforms This study presents the f i r s t simultaneous recordings of blood pressure and flow pulses in a cephalopod mollusc. The results provide dir e c t evidence that the systemic aorta in Octopus d o f l e i n i functions as a central e l a s t i c reservoir, just as predicted from the mechanical properties of the vessel wall. Complex transmission l i n e phenomena, which cause amplification and d i s t o r t i o n of the t r a v e l l i n g pressure pulse in the mammalian a r t e r i a l tree, were not evident in the octopus systemic c i r c u l a t i o n . Instead, the aort i c pressure pulse in 0. d o f l e i n i followed a near exponential decay in dias t o l e , and there were no indications of the occurrence of a secondary peak, nor any major a l t e r a t i o n in the pressure p r o f i l e as the wave t r a v e l l e d peripherally. Consequently, the simple, two element Windkessel (Fig. 5.1) can be used to describe hemodynamic relationships in the octopus aorta. The d i v i s i o n between systole and diastole was- not well defined in blood pressure and flow records from the octopus, as shown by the examples in Figures 5.4 and 5.5. This in agreement with the results of previous studies of blood pressure in t h i s species (Johansen and Martin, 1962) and other cephalopods (Bourne et a l . , 1978; Wells, 1979; Bourne, 1982). It has been suggested that the lack of an incisura in the a o r t i c pressure pulse may be due to differences in the-functional anatomy of the a o r t i c valve in cephalopods 200 compared to those in vertebrates (Johansen and Martin, 1962). While t h i s i s possible, the fact that the recording s i t e was several cm downstream from the heart, and therefore peripheral to a substantial portion'of the e l a s t i c reservoir provided by the aorta, would undoubtedly contribute to the disappearance of an incisura and flow reversal which may well occur adjacent to the heart. This pulse-smoothing phenomenon i s seen in flow pulses recorded from the pulmonary a r t e r i e s of t u r t l e s (Shelton and Burggren, 1976) and the ventral aorta of f i s h (Jones, et a l . , 1974). The importance of the location of the flow measuring s i t e within the a r t e r i a l tree i s demonstrated by model flow curves which are predicted from the measured pressure pulse (Fig. 5.9). Here, flow through the simple Windkessel i s transformed from a highly p u l s a t i l e waveform at the inflow, Qin, to a r e l a t i v e l y steady outflow, Qr, across the peripheral resistance. The measured flow pulse, Q(t), appears to be t r a n s i t i o n a l between inflow and outflow in i t s amplitude and phase. On the other hand, the measured pressure pulse, P ( t ) , was v i r t u a l l y unchanged as i t was propagated along the aorta (Fig. 5.10). It i s interesting that the predicted input pulse Qin (which i s equivalent to ventricular outflow), takes a form that i s almost i d e n t i c a l to the flow pulse in the ascending aorta of mammals (McDonald, 1974). That i s , at the onset of systole Qin rises with rapid acceleration to a sharp peak, then f a l l s through the remainder of systole, becoming 201 negative for a short period, and returning to zero for the l a t t e r two-thirds of diastole (Fig. 5.9). Thus, the observed pressure p r o f i l e in the octopus aorta ( i . e . one with no incisura) is consistent, in terms of the Windkessel model, with a ventricular outflow pattern that shows a d i s t i n c t period of reversal at the end of systole. Therefore i t i s not necessary to postulate that a o r t i c valves in cephalopods are functionally d i f f e r e n t from those in vertebrates, at least not with respect to closure being associated with a flow reversal. 2. Reflection Effects on Wave Velocity and Impedance The fundamental feature of the octopus c i r c u l a t i o n which allows the system to be i n f l a t e d by the heart as a single e l a s t i c reservoir, rather than as a complex transmission l i n e , i s that the components of the pressure pulse have wavelengths which are long compared to the aorta. The combination of these waves with strong r e f l e c t i o n s gives r i s e to a pressure pulse which appears to t r a v e l at very high v e l o c i t i e s . Thus, in vivo, C was considerably larger than the c h a r a c t e r i s t i c wave ve l o c i t y Co. S i m i l a r l y , the deviation in the in vivo impedance data from the c h a r a c t e r i s t i c value, Zo, was attributed to the presence of re f l e c t e d waves in the system. A brief consideration of some aspects of wave r e f l e c t i o n may help explain how these anomalies in v e l o c i t y and impedance occur (for d e t a i l s see McDonald, 1974, and 202 Milnor, 1982). It i s most convenient to consider the pressure wave in terms of i t s sinusoidal components. Reflected waves w i l l be generated in the aorta by mismatched impedances, the predominant source being the terminal resistance. If the terminus i s completely closed, the refl e c t e d wave w i l l be in phase with the incident wave at the s i t e of r e f l e c t i o n , and the amplitudes w i l l add together. If there i s a continuous t r a i n of pressure o s c i l l a t i o n s then, at a point one-quarter wavelength upstream from the r e f l e c t i o n s i t e , the incident wave w i l l be one quarter cycle e a r l i e r but the refl e c t e d wave w i l l be one quarter cycle l a t e r . The two waves w i l l therefore d i f f e r by one half cycle, or 180 degrees, and their amplitudes cancel and give a minimum. If the refl e c t e d wave is not attenuated, then the pressure o s c i l l a t i o n s seen at th i s point w i l l be zero. The waves w i l l again be in phase at a distance of one half wavelength from the terminus, and the amplitudes w i l l sum together to give another maximum. Points of minimum and maximum amplitudes c a l l e d nodes and antinodes, respectively, w i l l occur alternately at quarter wavelength int e r v a l s along the length of the tube (McDonald, 1974). In the aorta, r e f l e c t i o n s w i l l be p a r t i a l since the termination i s not completely closed (this was also the case in the in v i t r o experiments). P a r t i a l r e f l e c t i o n in a system with viscous damping, l i k e the aorta, w i l l give r i s e to a ref l e c t e d wave which is not completely in phase with the incident wave, thus s h i f t i n g the location of the e f f e c t i v e nodes and antinodes s l i g h t l y (Taylor, 1966a,b). 203 The interaction of the foreward and retrograde waves w i l l produce o s c i l l a t i o n s in pressure amplitude along the length of the aorta, and also o s c i l l a t i o n s in the phase s h i f t (and therefore the apparent velocity) of the resultant wave (Taylor, 1957a,b; McDonald, 1974). These o s c i l l a t i o n s w i l l be above and below the true values which would be measured i f there were no r e f l e c t i o n s . Like the pressure amplitude, the apparent v e l o c i t y w i l l also have a maximum at the r e f l e c t i o n s i t e (where the least phase change occurs), and a minimum at a point one quarter wavelength upstream (where the greatest phase s h i f t occurs). Additional nodes and antinodes w i l l alternate at successive quarter wavelength intervals along the tube. In the aorta, incident and r e f l e c t e d waves w i l l be attenuated as they t r a v e l , due to viscous losses. This w i l l cause the amplitude of o s c i l l a t i o n s in pressure and apparent ve l o c i t y to become more damped as the distance, in wavelengths, between the r e f l e c t i o n s i t e and the point of observation i s increased (Taylor, 1966b; McDonald, 1974). Thus, at high frequencies (short wavelengths), the apparent ve l o c i t y in the aorta w i l l approximate the c h a r a c t e r i s t i c , r e f l e c t i o n - f r e e value. It i s now clear that wavelength is the c r i t i c a l parameter in the analysis of pressure wave v e l o c i t y in a tube of f i n i t e length. It has already been noted that in vivo pressure wavelengths in the octopus are many times longer than the aorta. In Figure 5.12 the measurements of C are summarized, along with the predicted curves for Co at 204 F i g u r e 5.12. Apparent v e l o c i t y curves ( s o l i d l i n e s ) from the data of F i g u r e 5.11, p l o t t e d with the p r e d i c t e d c h a r a c t e r i s t i c v e l o c i t y Co (broken l i n e s ) f o r 30 and 60 cm of water p r e s s u r e . Frequency s c a l e (upper a b c i s s a ) has been transformed i n t o the r e l a t i v e wavelength based on Co, f o r each p r e s s u r e (lower a b c i s s a e ) . Arrows i n d i c a t e the frequency range of harmonics of the i n v i v o p r e s s u r e p u l s e . 205 pressures of 30 and 60 cm of water The frequency scale i s given in terms of wavelengths; s p e c i f i c a l l y , the r a t i o L /A i s plotted, where L is the tube length and A i s the wavelength. Frequency . and wavelength are inversely related, so that with increasing frequency L becomes a larger proportion of /\. As described above, the f i r s t minimum in C should occur at the frequency where L/A = 0.25. At a pressure of 30 cm of water L was 12 cm. Figure 5.12 shows that the quarter wavelength frequency, predicted from Co, was 5.2 Hz. The observed quarter wavelength frequency f e l l between 5 and 6 Hz, as indicated by the minimum in C and the maximum in transmission r a t i o (Figs. 5.11A & 5.12). Transmission r a t i o peaks at the nodal frequency because the upstream pressure i s at i t s minimum and the downstream pressure is at i t s maximum, a condition described as a p a r t i a l resonance (Taylor, 1966a). The good agreement between predicted and observed quarter wavelength frequency for the aorta is taken as a v e r i f i c a t i o n of the measurements of E'. Above th i s frequency the o s c i l l a t i o n in C around Co appeared to be highly damped. At 10 Hz (about the half wavelength frequency) C was only s l i g h t l y higher than Co. Below the quarter wavelength frequency, however, the path length becomes very small in r e l a t i o n to the wavelength, so that in the physiological frequency range L/X was less than 0.05, and consequently C rose to anomalously high values. Results of tests at 60 cm of water can be interpreted as showing the same behaviour as was seen at the lower 206 pressure, when frequency is expressed as the r a t i o L/A . Since Co i s increased with pressure a l l wavelengths are likewise increased. This results in the quarter wavelength frequency being extended to about 15 Hz, and L/A being decreased s t i l l further in the physiological range. Although i t was not possible to demonstrate the nodal frequency experimentally at this pressure, with some extrapolation the data suggest that at 15 Hz C meets Co, and thi s must be close to the minimum in C . The results of these experiments should be applicable to the in vivo c i r c u l a t i o n , with due consideration to the following factors: (1) the length of the test specimen was about 80% of the entire aorta, and (2) the preparation was perfused with sea water, which has a v i s c o s i t y about one-third that of octopus blood. Increasing the tube length and the f l u i d v i s c o s i t y w i l l tend to reduce the nodal frequency and transmission ratios somewhat (Taylor, 1966a,b). Therefore we may estimate that in vivo the minimum of C would f a l l just below 4 Hz, and the general conclusions w i l l be l i t t l e affected. That i s , in vivo the s i g n i f i c a n t harmonic components in the pressure pulse w i l l have wavelengths which range from 10 to 200 times longer than the entire aorta. This means the heart is separated from the major peripheral branch s i t e s by a distance which i s less than 1% of the wavelength of the fundamental frequency. Over this short distance, anomalies due to re f l e c t e d waves w i l l give r i s e to apparent wave v e l o c i t i e s which are 15 to 20 times higher than the true 207 wave v e l o c i t y as determined by the vessel e l a s t i c i t y . By virtue of r e f l e c t i o n s , the high compliance of the aorta i s preserved, while the e f f e c t i v e wave ve l o c i t y i s greatly elevated. Thus, in the octopus, the aorta w i l l indeed be in f l a t e d in v i r t u a l synchrony throughout, as a single e l a s t i c reservoir. O s c i l l a t i o n s in the input impedance of a v i s c o e l a s t i c tube also occur at quarter wavelength intervals because of r e f l e c t i o n e f f e c t s . A ref l e c t e d flow wave from a closed type of termination w i l l be negative, since the sign indicates the dir e c t i o n of t r a v e l . This i s equivalent to a 180 degree phase s h i f t with respect to the incident wave. Therefore, the flow amplitude w i l l be minimal at the termination (zero i f the end is completely closed), and maximal at a point one quarter wavelength upstream. Pressure amplitude, on the other hand, w i l l be maximal at the termination and minimal at the quarter wavelength position. This means that nodes of flow coincide with antinodes of pressure, and vice versa (McDonald, 1974). Thus impedance modulus, which i s the r a t i o of pressure to flow amplitudes, shows a pattern of o s c i l l a t i o n with increasing frequency which i s similar to the o s c i l l a t i o n s of pressure amplitude and apparent v e l o c i t y , as described above. That i s , impedance modulus i s high at very low frequencies ( i t equals the terminal resistance at zero frequency), and f a l l s to a minimum at the quarter wavelength frequency. Further o s c i l l a t i o n s in impedance modulus at multiples of the quarter wavelength frequency are damped by wall and f l u i d 208 v i s c o s i t y , so that at high frequencies the impedance modulus se t t l e s to approximately Zo, the r e f l e c t i o n - f r e e value. It i s well established that these predicted patterns in apparent wave ve l o c i t y and impedance modulus do occur in the mammalian aorta and in transmission l i n e models (McDonald, 1974; Milnor, 1982), because a l l harmonics above the fundamental are higher than the quarter wavelength frequency (Noordergraaf et a l . , 1979). In contrast, the in vivo frequencies of pressure pulsation in the octopus systemic c i r c u l a t i o n are well below the quarter wavelength frequency. Accordingly, the octopus aorta behaves l i k e a Windkessel, and as predicted, /Z/ and C both are well above their c h a r a c t e r i s t i c values. The major differences between Windkessel and transmission l i n e models arise because the range of frequencies, or more s p e c i f i c a l l y the range of L/X values, which occurs i s much lower in the former than in the l a t t e r . Thus the Windkessel may be regarded as a special case of transmission l i n e (Noordergraaf, 1978). 3. The Input Impedance in the Octopus Windkessel The variation in impedance modulus with frequency in a transmission l i n e varies c l o s e l y with the apparent wave ve l o c i t y , for reasons discussed above. Just as Zo is d i r e c t l y proportional to Co (eqn. 5.14), /Z/ may be calculated from C by a similar r e l a t i o n (McDonald, 1974). In Figure 5.13 the predicted impedance spectrum i s plotted for the octopus aorta (broken l i n e ) . This curve was calculated from values of C 209 Lf) E 1 O CD I/) c u c -5 1 0 TD O .5 .1 0> £ .05 o *o CD C L E .01L 0.1 A A NIZI \ \ \ J — I — I — I I I I I 1.0 Frequency (Hz) J — i — i — i • i i i t 10 F i g u r e 5.13. C a l c u l a t e d impedance modulus curve (broken l i n e ) , based on the data f o r C i n F i g u r e 5.12 f o r a pre s s u r e of 30 cm of water, compared wi t h the curve f o r Zo ( s o l i d l i n e ) p r e d i c t e d from the dynamic mechanical p r o p e r t i e s of the a o r t a (equation 5.14). The data p o i n t s are measured values of /Z/ from an octopus i n which the mean pre s s u r e was 30 cm of water. 210 measured in v i t r o at a mean pressure of 30 cm of water and then shifted so that the quarter wavelength frequency f a l l s at the estimated in vivo value of 4 Hz. The impedance data from one octopus in which mean pressure was also 30 cm of water are plotted as well, and reasonable agreement i s seen between the observed and predicted impedances at least at the low frequencies where in vivo data is a v a i l a b l e . This Figure i l l u s t r a t e s the inherent disadvantage of the Windkessel system. That i s , since the heart rate i s well below the quarter wavelength frequency, the impedance to p u l s a t i l e flow is always well above the l e v e l which could be experienced by the heart i f frequencies were much higher. In mammals, due to the much higher heart rates, the heart i s functionally uncoupled from the high peripheral resistance at harmonics above the second. At these frequencies the mammalian heart "sees" an input impedance which approximates that of a r e f l e c t i o n - f r e e system, and the t o t a l p u l s a t i l e work is reduced (Taylor, 1964; Noordergraaf et a l . , 1979). Presumably, at higher heart rates the octopus could also experience a similar uncoupling of the heart from the peripheral resistance, but inspection of Figure 5.13 shows that t h i s would require at least a. ten-fold increase in the cardiac frequency. It seems unlikely that the increased energy cost associated with such an elevated heart rate would be outweighed by the saving from reduced impedance. This same conclusion was proposed previously by L a n g i l l e and Jones 21 1 (1977) in their assessment of hemodynamics in the frog. It i s interesting to speculate that cephalopods which are much more active and larger than 0. d o f l e i n i , such as large pelagic squids, may well have c i r c u l a t o r y systems which have wave transmission c h a r a c t e r i s t i c s much l i k e those of mammals. 212 CHAPTER VI. SUMMARY This study gives a detailed description of the mechanical properties of the aorta of a cephalopod mollusc, from three d i f f e r e n t levels of investigation: 1) the physical and chemical properties of an e l a s t i c connective tissue component of the artery wall, 2) the v i s c o e l a s t i c properties of the whole artery wall in v i t r o and 3) the influence of the mechanical behaviour of the aorta on the dynamics of blood flow in vivo. Presumptive e l a s t i c f i bres were i d e n t i f i e d h i s t o l o g i c a l l y , in the octopus aorta, by their a f f i n i t y for aldehyde-fuchsin s t a i n . These fibres are found in an internal e l a s t i c a (IE) on the adlumenal surface, beneath an incomplete endothelial c e l l layer. Electron microscopy showed that a network of these f i b r e s occurs e x t r a c e l l u l a r l y throughout the the a o r t i c wall, and appears to be continuous with the IE. Fibres in the IE were isolated by dissection, and by chemical extraction of the artery wall. These fibres were subjected to a series of chemical and mechanical tests, with the following r e s u l t s . The fibres are composed almost exclusively of a protein which i s rubber-like, that i s , a material which has high e x t e n s i b i l i t y , and an e l a s t i c modulus of the same magnitude as that of l i g h t l y crosslinked natural rubber. Further, the octopus e l a s t i c protein appears to have covalently crosslinked and k i n e t i c a l l y free molecular chains which clo s e l y approximate the thermoelastic behaviour of a 213 polymer with entropic (i.e rubber-like) e l a s t i c i t y . The amino acid composition of the octopus e l a s t i c protein readily distinguishes i t from other known protein rubbers ( e l a s t i n , r e s i l i n , abductin), and therefore i t i s proposed that this previously undescribed protein be c a l l e d the octopus a r t e r i a l elastomer (OAE). In v i t r o tests of the s t a t i c and dynamic mechanical properties of the octopus aorta demonstrated that this blood vessel i s a highly d i s t e n s i b l e r e s i l i e n t e l a s t i c tube. A very important feature of the octopus aorta i s that the e l a s t i c i t y i s markedly non-linear, that i s , the vessel wall becomes s t i f f e r with increasing extension. In t h i s respect the octopus aorta i s equivalent to the blood vessels of vertebrate animals. Non-linear e l a s t i c i t y allows the artery to be compliant at low physiological pressures, but to be protected from aneurisms and rupture at higher pressures. The importance of a r t e r i a l compliance to c i r c u l a t o r y dynamics in mammals and other vertebrates is well appreciated. Primarily, the p u l s a t i l e flow of blood from the heart i s smoothed to a steady flow at the peripheral vascular beds by the passive e l a s t i c i t y of the large a r t e r i e s . In addition, wave propagation c h a r a c t e r i s t i c s such as velocity and attenuation are greatly influenced by the v i s c o e l a s t i c i t y of the artery wall. However, these important factors have not previously been investigated d i r e c t l y in any invertebrate c i r c u l a t o r y system. In t h i s study, in vivo measurements of blood pressure and flow, and pressure wave v e l o c i t y show that 214 the octopus a r t e r i a l c i r c u l a t i o n can be adequately described as a single central e l a s t i c reservoir (the aorta) which i s charged intermittantly by flow from the heart, and which discharges through a single r e s i s t o r (the peripheral vasculature) while the heart r e f i l l s . This study has shown that in many ways the mechanical design of the octopus aorta p a r a l l e l s that of vertebrate blood vessels. At physiological pressures the high d i s t e n s i b i l i t y and e l a s t i c i t y of the artery wall is provided by rubber-like proteins, e l a s t i n in the vertebrates and OAE in the cephalopod. The physical and chemical properties of these two proteins are remarkably similar yet the amino acid compositions, and presumably the primary structure, are very d i f f e r e n t in e l a s t i n and OAE. This suggests that these proteins evolved independently in the two groups, perhaps at the same time and in response to the same selection pressure. F o s s i l evidence indicates that the coleoid cephalopods succeded the more primitive ammonite forms about 150 m i l l i o n years ago, around the time of the expansion of teleost f i s h in the sea. The modern f i s h and cephalopods evolved together and i t seems l i k e l y that they became dire c t competitors in the same environments (Packard, 1972). One result of this competition may have been the development of the high pressure closed c i r c u l a t o r y system in cephalopods to support their elevated metabolic rate and more powerful locomotory c a p a b i l i t i e s , compared to the primitive ammonites, and the incorporation of a protein rubber into the artery wall for 215 increased e f f i c i e n c y of blood c i r c u l a t i o n . 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