UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A study of biophysical phenomena associated with gas bubble trauma in fish Fidler, Larry E. 1985

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1985_A6_7 F53.pdf [ 4.5MB ]
Metadata
JSON: 831-1.0096083.json
JSON-LD: 831-1.0096083-ld.json
RDF/XML (Pretty): 831-1.0096083-rdf.xml
RDF/JSON: 831-1.0096083-rdf.json
Turtle: 831-1.0096083-turtle.txt
N-Triples: 831-1.0096083-rdf-ntriples.txt
Original Record: 831-1.0096083-source.json
Full Text
831-1.0096083-fulltext.txt
Citation
831-1.0096083.ris

Full Text

A STUDY OF BIOPHYSICAL PHENOMENA ASSOCIATED WITH GAS BUBBLE TRAUMA IN FISH bys L a r r y E. F i d l e r B . S c . P e n n s y l v a n i a S t a t e U n i v e r s i t y , P e n n s y l v a n i a USA, 1960 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We a c c e p t t h i s t h e s i s as con-forming t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA JULY 1985 © Lawrence E. F i d l e r , 1985 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of T£&0£-0(2- 7 The University of British Columbia 1956 Main Mali Vancouver, Canada V6T 1Y3 Date 0C7 / /9fS~ DE-6(3/81) ABSTRACT The condition of Gas Bubble Trauma i n f i s h was examined in terms of s p e c i f i c symptoms involving bubble development i n the c i r c u l a t o r y system and buccal c a v i t i e s of f i s h . Based on a comparison between the conditions for bubble growth i n f i s h exposed to supersaturated water and mammals exposed to hyperbaric and hypobaric decompression a mathematical model was developed describing environmental water threshold needed to i n i t i a t e bubble growth i n f i s h . The equation development yielded expressions which related the thresholds i n t o t a l dissolved gas pressure required to i n i t i a t e bubble growth i n the c i r c u l a t o r y system to the p a r t i a l pressure r a t i o of dissolved oxygen in the environmental water, oxygen uptake r a t i o across the g i l l , the size of nucleation s i t e s i n the c i r c u l a t o r y system, the surface tension of f i s h blood and environmental parameters such as water temperature, depth and barometric pressure. In the case of bubble growth i n the buccal cavity, environmental water thresholds were related to t o t a l gas pressure, nuclei radius, water surface tension, water temperature, depth and barometric pressure. Bubble growth thresholds were examined for a range of the above dependent parameters. TABLE OF CONTENTS Page Number Abstract i i . Table of Contents i i i . L i s t of Tables v. L i s t of Figures v i . L i s t of; Symbols v i i . Acknowledgments ix. 1.0 Introduction 1 1.1 Symptoms and Causes 1 1.2 Problem Statement 4 1.3 Current Study 8 2.0 Preliminary Considerations 10 2.1 GBT i n f i s h and other forms of decompression 12 2.1.1 Source and quantity of dissolved gas 12 2.2 Circulatory system bubbles i n hyperbaric and hypobaric decompression 13 2.3 Circulatory system bubbles i n GBT 15 2.3.1 Exposure to supersaturation 15 2.3.2 A r t e r i a l vs. venous blood 17 2.4 Vascular system bubble gases 19 2.4.1 Nitrogen 19 2.4.2 Oxygen 20 2.4.3 Carbon Dioxide 21 2.4.4 Water vapor 22 2.5 Nucleation s i t e s and bubble growth 22 2.6 Nucleation models 26 2.6.1 The Harvey model 26 2.6.2 The Fox and Herxfeld model 27 2.6.3 Nucleation s i t e size 28 2.6.4 Surface tension 29 i i i . 3.0 Methods 31 3.1 Bubble growth equations 31 3.1.1 Assumptions 34 3.2 Equation Development 35 3.3 Experimental surface tension measurement 48 4.0 Results 52 4.1 Threshold analysis - environmental water 52 4.2 Threshold analysis - a r t e r i a l blood 54 4.2.1 Surface Tension 54 4.2.2 K - Transport Parameters 56 4.2.3 Pe - Bubble external pressure 56 4.2.4 A r t e r i a l blood thresholds 57 4.2.5 Venous blood thresholds 59 5.0 Discussion 61 5.1 Bubble growth thresholds 61 5.1.1 Water 61 5.1.2 A r t e r i a l Blood 62 5.1.3 Venous Blood 63 5.2 Parametric forms 63 5.2.1 K - Transport parameters 63 5.2.2 F - Oxygen uptake r a t i o 64 5.2.3 X'o - Oxygen p a r t i a l pressure r a t i o 66 5.2.4 Sur face tens ion 68 5.2.5 Exposure to supersaturation 69 5.3 Nucleation s i t e s - free or fixed 70 5.4 Conclusion 76 6.0 References 79 7.0 Appendix A H I i v . LIST OF TABLES Page No. TABLE 1 Bubble Growth Equations 33 TABLE 2 Fish Blood Surface Tension Calculations 55 v. LIST OF FIGURES Page Number Figure No.l Laplaces Equation for a gas bubble i n Water 90 Figure No.2 Nucleation Sites as a function of Supersaturation ...91 Figure No.3 Surface Tension of Water and Human Blood 92 Figure No.4 Pendant Drop of Blood with Dimension Parameters 93 Figure No.5 Surface Tension Measurement Experimental Apparatus ..94 Figure No.6 Water TGP Thresholds Versus Temperature Alt.= S.L....95 Figure No.7 Water TGP Thresholds Versus Temperature Alt.= 700 M..96 Figure No.8 Water TGP Thresholds (LOC) Versus Temperature,700 M..97 Figure No.9 TGP Thresholds Versus Compensation Depth, Alt.= S.L..98 Figure No.10 Surface Tension of Fish Blood 99 Figure No.11 Variation of Transport Ratios with Temperature ....100 Figure No.12 TGP Thresholds for A r t e r i a l Blood vs. X'o (F=0.33).101 Figure No.13 TGP Thresholds for A r t e r i a l Blood vs. X'o (F=0.67).102 Figure No.14 TGP Thresholds for A r t e r i a l Blood vs. X'o (F=0.85) 103 Figure No.15 TGP Thresholds for A r t e r i a l Blood vs. X'O (700 M) .104 Figure No. 16 TGP Thresholds for A r t e r i a l Blood vs 0=» Uptake ....105 Figure No.17 Compensation Depth for A r t e r i a l Blood (F=0.33) ....106 Figure No.18 Compensation Depth for A r t e r i a l Blood (F=0.67) ....107 Figure No.19 Compensation Depth for A r t e r i a l Blood (F=0.85) ....108 Figure No.20 TGP Threshold for A r t e r i a l Blood with Pa - 40 mmHg.109 Figure No.21 TGP Thresholds for Venous Blood Versus X'o 110 \ v i . L I S T O F S Y M B O L S A - H O D O L - R T B - T G P t F X ' o + K ( l - X ' o ) ] C - F X ' o + K ( l - F X ' o ) D - P e - P H 2 o DOI_,IMI_ - D i f f u s i v i t y o f o x y g e n o r n i t r o g e n i n s o l u t i o n D A I _ , B U . - D i f f u s i v i t y o f g a s e o u s s p e c i e s A o r B i n s o l u t i o n D e - M a x i m u m p e n d a n t d r o p d i a m e t e r D s - P e n d a n t d r o p d i a m e t e r a t d i s t a n c e D e a b o v e d r o p v e r t e x E - B - C * P e F - O x y g e n u p t a k e r a t i o a c r o s s g i l l s F ' - S h a p e f a c t o r i n p e n d a n t d r o p s u r f a c e t e n s i o n e q u a t i o n h - D e p t h b e l o w w a t e r s u r f a c e H A , B - H e n r y s c o n s t a n t f o r g a s e o u s s p e c i e s A o r B i n s o l u t i o n H O . I M = H e n r y s c o n s t a n t f o r o x y g e n o r n i t r o g e n i n s o l u t i o n He - C o m p e n s a t i o n d e p t h i n m e t e r s k - M a s s t r a n s f e r r e s i s t a n c e k i _ - L i q u i d p h a s e m a s s t r a n s f e r c o e f f i c i e n t K - M a s s t r a n s p o r t p a r a m e t e r L 2oC N a % - P a r t i a l p r e s s u r e o f d i s s o l v e d n i t r o g e n - p e r c e n t o f e q u i l i b r i u m n ^ . E . - M o l e s o f g a s e o u s s p e c i e s A o r B i n b u b b l e 0:2% - P a r t i a l p r e s s u r e o f d i s s o l v e d o x y g e n - p e r c e n t o f e q u i l i b r i u m P A . B - P a r t i a l p r e s s u r e o f g a s e o u s s p e c i e s A o r B i n b u b b l e P ^ o , B O - P a r t i a l p r e s s u r e o f g a s e o u s s p e c i e s A o r B i n s o l u t i o n P a t m . - A t m o s p h e r i c p r e s s u r e P B - C a v i t y p r e s s u r e P e - B u b b l e e x t e r n a l p r e s s u r e c o m p o s e d o f a t m o s p h e r i c , h y d r o s t a t i c a n d s y s t e m p r e s s u r e P H 2 o - P a r t i a l p r e s s u r e o f w a t e r v a p o r i n b u b b l e a t t e m p e r a t u r e T P R - B u b b l e i n t e r n a l p r e s s u r e P P - E - P e c l e t n u m b e r P ' O O . N O - P a r t i a l p r e s s u r e o f o x y g e n o r n i t r o g e n i n w a t e r Q - ( P e + (26/ro)) •R - U n i v e r s a l g a s c o n s t a n t r - B u b b l e r a d i u s T - A b s o l u t e t e m p e r a t u r e T G P - t o t a l p r e s s u r e o f a l l d i s s o l v e d g a s e o u s s p e c i e s TGP% - T o t a l p r e s s u r e o f a l l d i s s o l v e d g a s e s a s p e r c e n t o f e q u i l i b r i u m t - t i m e Uo - V e l o c i t y o f f l u i d m o v i n g r e l a t i v e t o b u b b l e X A , B - M o l e f r a c t i o n o f g a s e o u s s p e c i e s A o r B i n b u b b l e X ' o - p a r t i a l p r e s s u r e r a t i o o f o x y g e n i n s o l u t i o n Y ( r ) - S t r e n g t h o f o r g a n i c s k i n 6 - S u r f a c e t e n s i o n o f f l u i d i n w h i c h b u b b l e i s g r o w i n g p - W a t e r d e n s i t y Ob - B l o o d d e n s i t y p « - A i r d e n s i t y 1J  - H E J D E J L . [ P B O + P H 2 O - ( P E + (267r ) ) ( l - x * ) ] 0 - H A D A L . C P A O - X A ( P E + (267r))] IT. - P i = 3 . 1 4 1 5 9 v i i i . A C K N O W L E D G M E N T S T h e a u t h o r w i s h e s t o e x p r e s s h i s a p p r e c i a t i o n t o t h e m a n y p e o p l e w h o h e l p e d i n t h e a c c o m p l i s h m e n t o f t h i s w o r k . I n p a r t i c u l a r , t h a n k s a r e d u e t o p e r s o n a l o f t h e P a c i f i c B i o l o g i c a l S t a t i o n ; D r . D o n A l d e r d i c e a n d M r . J o h n J e n s e n , a n d M r . B i l l M c L e a n o f t h e S a l m o n E n h a n c e m e n t P r o g r a m . T h e i n f o r m a t i o n t h e y p r o v i d e d a n d t h e m a n y s t i m u l a t i n g d i s c u s s i o n s a d d e d t o t h e a u t h o r s u n d e r s t a n d i n g o f t h e G B T p r o b l e m s f r e q u e n t l y e n c o u n t e r e d i n t h e h a t c h e r y . T h e a u t h o r i s p a r t i c u l a r l y i n d e b t e d t o D r . D a v i d R a n d a l l a n d t h e p e r s o n n e l o f h i s l a b o r a t o r y a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . T h e w o r k d e s c r i b e d i n t h i s t h e s i s w a s f u n d e d i n p a r t b y t h e C a n a d a D e p a r t m e n t o f F i s h e r i e s a n d O c e a n s , S a l m o n i d E n h a n c e m e n t P r o g r a m - C o n t r a c t N o . O S B 8 3 - 0 0 3 4 0 1.0 INTRODUCTION The syndrome of Gas Bubble Trauma i n f i s h and aquatic invertebrates has been the subject of extensive study over the past two decades. The condition i s the r e s u l t of separation from the solution state of atmospheric gases dissolved i n a supersaturated condition i n body f l u i d s and ti s s u e . In other words, bubbles of gas develop i n t i s s u e , organs, body c a v i t i e s and the vascular system of aquatic animals. In many ways the processes and symptoms of Gas Bubble Trauma (referred to as GBT throughout the remainder of t h i s thesis) c l o s e l y resemble those associated with decompression sickness encountered i n human divers, caisson workers, p i l o t s and experimental animals{however, with important differences. 1.1 SYMPTOMS AND CAU8E8 Much of what i s currently known about GBT comes from studies of damage to f i s h populations r e s u l t i n g from dissolved gas supersaturation induced by man made a l t e r a t i o n s to natural water courses. For example, hydroelectric development projects on the Columbia River i n the United States produced high l e v e l s of supersaturation i n the discharge from dam spillways. Total dissolved gas pressures approaching 1.5 atmospheres were common and produced major m o r t a l i t i e s i n migrating Salmonid stocks <Becker, 1973; Beiningen and Ebel, 1970; Beiningen and Ebel, 1971; Boiick et a l . , 1970; Blahm et a l . , 1975 and Ebel, 1979). At these l e v e l s of supersaturation several forms of physiological i n s u l t 1 are thought to lead to mortality. These include bubbles i n the c i r c u l a t o r y system (embolisms) with various degrees of blockage and hemostatis, bubble produced lesions of ti s s u e and organs and ov e r - i n f l a t i o n of body c a v i t i e s (tympanites). Other symptoms such as i n f e c t i o n caused by b l i s t e r i n g and lesions of the skin and exophthalmia induced s u s c e p t i b i l i t y to predation are considered to be secondary contributors to mortality. There may be other more subtle symptoms that contribute to mortality such as damage to blood structure and c l o t t i n g at the interface of blood with vascular system bubbles ( C a s i l l a s et a l . , 1975 and C a s i l l a s et a l . , 1976). At the acute l e v e l s of supersaturation encountered on the Columbia River, the time course f o r mortality varied from hours to days depending on the level of dissolved gas tension. More recently, attempts to enhance Salmonid stocks i n Canada through programs of hatchery incubation and rearing have brought to l i g h t the e f f e c t s of supersaturation on young f i s h . With the increased use of well and spring water far incubation and rearing, hatchery water sources are frequently supersaturated to the extent that the t o t a l pressure of a l l dissolved gases exceeds atmospheric pressure by up to 1.3 atmospheres (Shepherd and MacDonald, 1980). Unless properly aerated to reduce dissolved gas tension, t h i s water w i l l produce symptoms of swim bladder and i n t e s t i n a l c a v i t y o v e r — i n f l a t i o n , bubbles i n the c i r c u l a t o r y system, bubble produced lesions and b l i s t e r i n g of the f l e s h , o v e r - i n f l a t i o n and suspected coagulation of alevin yolk sacs and bubbles i n the buccal cavity, (Weitkamp and Katz, 1980; Stroud et a l . , 1975; Shirahata, 1966 ; Harding, 1984 and Jensen, 1984). 2 Again these symptoms p r e c i p i t a t e mortality i n time periods ranging •from hours to weeks depending on the level o-f dissolved gas tension. The hatchery experience has demonstrated that i n -fish such as salmonids and most t e l e o s t s , the early stages of development are l i f e stages p a r t i c u l a r l y s e n s i t i v e to problems involving supersaturation (Bouck et a l . , 1975; Shirahata, 1966; Meeken and Turner, 1974; Jensen, 1980; Harding, 1984 and Dawley et a l . 1976). This of course places even higher demands on the q u a l i t y of water used i n f i s h hatcheries. It further implies that constraints more r e s t r i c t i v e than have been exercised i n the past must be applied to projects involving the modification of water courses for hydroelectric development or other purposes. In the past, the e f f e c t s of such projects focused on adult f i s h where large m o r t a l i t i e s were e a s i l y detected. In the case of young f i s h , due to t h e i r s i z e and predation pressure, large m o r t a l i t i e s created by the e f f e c t s of supersaturation could go v i r t u a l l y undetected. The consequences of such losses on Salmonid Enhancement Programs and the maintenance of wild stacks are a l l too apparent. The r e s u l t s of the many studies that were conducted in r e l a t i o n to supersaturation on the Columbia River, supersaturation i n hatcheries and other work i n the f i e l d of GBT can be found summarized i n the review works of Weitkamp and Katz, 1980; Harvey, 1975 and Stroud et al.,1975. 3 1.2 PROBLEM STATEMENT In examining the large quantity o-f data associated with supersaturation i n -Fish, i t i s apparent that a great deal of v a r i a b i l i t y e x i s t s among the observations of the various researchers (Weitkamp and Katz, 1980). Much of t h i s i s the d i r e c t r e s u l t of reporting observations s o l e l y i n terms of water temperature, time to mortality and t o t a l gas pressure (T8P). TOP i s the t o t a l pressure of a l l dissolved gas species i n the environmental water. Unfortunately most experimental data has been c o l l e c t e d without regard to the fac t that other parameters are equally important i n determining whether the symptoms of GBT and m o r t a l i t i e s would occur. For example, Alderdice, Jensen and Schnute (1984) found that the r e l a t i v e concentrations of oxygen and nitrogen i n the water can have a s i g n i f i c a n t e f f e c t on TGP thresholds and the time course to mortality. In addition, data i s frequently presented without information regarding changes i n barometric pressure and water temperature occurring at the time the data was co l l e c t e d . Yet another important parameter i s depth of water available to the f i s h during the period of exposure. The importance of small changes i n these l a t t e r three variables w i l l be examined l a t e r i n t h i s section. Most important however, i s the lack of information as to whether mortality was the r e s u l t of bubbles i n the c i r c u l a t o r y system, o v e r - i n f l a t i o n of body c a v i t i e s or some of the other symptoms noted e a r l i e r . 4 E s s e n t i a l l y a l l symptoms and types of physiological i n s u l t are lumped together. Consequently, l i t t l e information i s avai l a b l e from these studies which r e l a t e s mortality to the conditions of c r i t i c a l physiological i n s u l t , s p e c i f i c symptoms, or detailed, environmental parameters. C r i t i c a l physiological i n s u l t i s defined as that physical mechanism which produces i r r e v e r s i b l e physiological damage and death. To i l l u s t r a t e the d i f f i c u l t y i n analyzing data from the l i t e r a t u r e , the P a c i f i c B i o l o g i c a l Station of the Canada Department of F i s h e r i e s and Oceans recently undertook an examination of the published data on GBT m o r t a l i t i e s in salmonids (Alderdice, Jensen and Schnute (1985). The purpose of t h i s study was to attempt to model the data with a generalized surface response analysis technique (Schnute and McKinnell, 1984). Of over 600 data points, approximately 90% were found to be unusable. Of the remaining 69 points, ET50 information (estimated time to 50% mor t a l i t y ) , was avai l a b l e with limited information on conditions of water temperature, depth, TGP, oxygen to nitrogen r a t i o s , species, s i z e and barometric pressure. Almost none of the data distinguished between types of physiological i n s u l t such as bubbles i n the c i r c u l a t o r y system, o v e r - i n f l a t i o n of the swim bladder or other symptoms. A d i s t i n c t i o n i n the type of physiological i n s u l t i s e s p e c i a l l y important when examining low l e v e l s of supersaturation and longer ET50 periods. For example, o v e r - i n f l a t i o n of the swim bladder can lead to added energy demands to carry on compensatory swimming. Young f i s h having the extra energy requirements of growth w i l l be at a s i g n i f i c a n t disadvantage i n dealing with t h i s problem compared to adult f i s h . 5 To date the e f f o r t s of the P a c i f i c B i o l o g i c a l Station to model these 69 experimental data points are incomplete. At t h i s time i t i s not known what l e v e l s of supersaturation can be tolerated by adult and juvenile Salmonids. The Environmental Protection Agency in the United States uses a c r i t e r i a that the TGP must be l e s s than 1.10 atmospheres for the Columbia River System (Weitkamp and Katz, 1980). Yet, i t i s known that t o t a l dissolved gas pressures as low as 1.03 to 1.06 atmospheres have produced symptoms of GBT and mortality i n small f i s h , (Colt and Cornacchia, 1982; Harding, 1984 and McLean, 1984). In some cases these data do not contain complete information on a l l environmental parameters associated with the appearance of the problem. Consequently, i t i s d i f f i c u l t to determine i f the symptoms were the r e s u l t of a mean TGP of 1.03 atmospheres, or whether other fac t o r s such as the dynamics of the environment contributed to the appearance of the condition. Yet, i n theoreti c a l work related to that of t h i s t h e s i s , F i d l e r (1984) has shown that the TGP threshold f o r the o v e r i n f l a t i o n of a f i s h e s swim bladder i s on the order of 1.03 atmospheres. At low l e v e l s of supersaturation the s e n s i t i v i t y of the appearance of GBT symptoms to the dynamics of the environment i s best i l l u s t r a t e d by three examples. 1.) Consider a water source which i s i n i t i a l l y at equilibrium with atmospheric a i r , at a temperature of 10 deg. C. and a barometric pressure of 760 mm Hg. ( 0=>X = 100%, N 3X = 6 100%, TGP = 1.0 atmospheres). A rapid increase i n water temperature of 2 deg. C. may cause dissolved gas tensions to becomes 0 Z % = 104.377., N2X = 104.78% and TGP = 1.046 atmospheres. 2. ) Consider yet another water source which i s at equilibrium with atmospheric a i r , a water temperature o-f 10 deg. C. and a barometric pressure of 760 mm Hg. A rapid decrease i n barometric pressure of 30 mm Hg. may produce dissolved gas tensions ofs 0 aX = 104.16%, N z% = 104.21% and a TGP = 1.042 atmospheres. 3. ) F i n a l l y , for the above l e v e l s of supersaturation, i . e . TGP = approximately 1.04 atmospheres, a water depth of le s s than 40 cm. w i l l provide enough compensation to prevent bubble formation. Here 0s»%, N 2% are the d e f i n i t i o n s of dissolved gas tension (per cent of equilibrium), commonly used throughout Canada Fi s h e r i e s and Oceans Salmonid Enhancement Program (McLean and Boreham, 1980). It i s clear that i f l e v e l s of supersaturation on the order of 1.03 atmospheres can induce symptoms of GBT i n small f i s h , then changes in parameters such as barometric pressure, water depth and fl u c t u a t i o n s i n water temperature may play c r i t i c a l r o l e s i n establishing what are safe l e v e l s i n the hatchery and i n natural water courses. Furthermore i f the conditions which lead to 7 mortality are to be understood, the symptoms must be examined i n d i v i d u a l l y and not lumped together as has been the practice i n past studies. A preliminary examination by t h i s author o-f the biophysical processes involved i n GBT suggests that each major symptom has unique pathways for the transport of dissolved gases to bubbles or c a v i t i e s ( F i d l e r , 1983). In addition, unique combinations of environmental, physiological and physical parameters may be required to i n i t i a t e the onset of each symptom and the corresponding time course to mortality. 1.3 Current Study In i n i t i a t i n g t h i s study, i t was considered that cer t a i n major symptoms of GBT could be analyzed using conventional biophysical and engineering approaches and that mathematical r e l a t i o n s h i p s could be developed which r e l a t e threshold conditions f o r s p e c i f i c symptoms to environmental water parameters and the physiological state of the f i s h . In p a r t i c u l a r , t h i s work was directed at examining those mechanisms which lead to bubble formation i n the c i r c u l a t o r y systems and external water environment of f i s h . The l a t t e r condition would apply to the e a r l i e r mentioned symptom of bubble formation i n the buccal cavity of small f i s h which has been observed by both Jensen (1980) and Shirhata (1966). The cause of mortality i n t h i s form of GBT i s thought to be blockage of respiratory water flow and suffocation. The two symptoms are phy s i c a l l y s i m i l a r i n that they involve bubble formation and growth i n a l i q u i d ; the blood i n one case and the environmental water i n the other. Bubble growth i n l i q u i d s has received 8 considerable attention i n the l i t e r a t u r e and the mechanism of bubble growth i s well understood at least conceptually. Mathematical descriptions of the process have not been applied to GBT i n f i s h . The study e f f o r t described herein consisted of three d i s t i n c t phases. F i r s t , before an attempt at a mathematical model could be j u s t i f i e d there were a number of conditions associated with bubble formation i n the c i r c u l a t o r y systems of f i s h which required c l a r i f i c a t i o n . Next, mathematical re l a t i o n s h i p s that describe the bubble growth processes i n the vascular system and the external water environment were derived for a two gas plus water vapor system. The equations were solved and examined i n terms of indicated thresholds and the s e n s i t i v i t y of these thresholds to the parameters c o n t r o l l i n g the bubble growth process. Complementing the a n a l y t i c a l e f f o r t was an experimental evaluation of the surface tension of f i s h blood. As w i l l be shown i n the Preliminary Considerations Section to follow, t h i s parameter i s of i c r i t i c a l importance to the a n a l y t i c a l model f o r c i r c u l a t o r y system bubble formation and only limited data e x i s t s for f i s h blood. 9 2.0 PRELIMINARY CONSIDERATIONS Be-Fore a mathematical model describing bubble growth thresholds could be developed, i t was necessary to clari-fy several important aspects o-F bubble growth i n -Fish exposed to supersaturated water. This c l a r i f i c a t i o n was required in order to esta b l i s h a v a l i d basis for the model and to determine cert a i n parametric forms which must be r e f l e c t e d i n the model. F i r s t , i t was necessary to esta b l i s h that a model which describes bubble growth i n a l i q u i d was indeed v a l i d f o r c i r c u l a t o r y system bubbles i n f i s h . Throughout the l i t e r a t u r e , bubble growth i n GBT i s often equated with that associated with hyperbaric and hypobaric decompression. For these l a t t e r forms of decompression, i t i s known that intravascular bubbles often o r i g i n a t e extravascularly and appear i n the vascular system as a r e s u l t of rupture in the vessel walls ( H i l l s , 1977). If bubble formation proceeded i n a s i m i l a r manner i n f i s h exposed to supersaturated water, i t would be inappropriate to develop a model f o r bubble growth i n a l i q u i d and then apply i t to bubbles i n the blood which in f a c t form i n ti s s u e adjacent to the vascular system. In t h i s regard, the differences between GBT i n f i s h and other forms of decompression have not been described c l e a r l y i n the l i t e r a t u r e . These differences determine not only the form of a threshold model but also the boundary and i n i t i a l conditions that w i l l apply. An equally important part of t h i s study involved an examination of the manner in which f i s h are exposed to supersaturated water. Variations i n both the symptoms and the time course to mortality 10 may e x i s t between those f i s h that are exposed to supersaturation at shallow depths and those that are exposed at greater depth and then moved to the surface. The distinguishing features of these two types of exposure w i l l become apparent i n the discussion to follow; however, to date the d i s t i n c t i o n has been absent i n the l i t e r a t u r e . As mentioned e a r l i e r i n regard to the GBT l i t e r a t u r e , dissolved gas tension i s most often reported i n terms of environmental water conditions only. It i s known however that, depending on the physiological state of a f i s h , the dissolved gas tension in i t s c i r c u l a t o r y system w i l l d i f f e r s u b s t a n t i a l l y from that of the environmental water, (Hoar and Randall 1970). Thus, i t i s important that a bubble growth threshold model r e f l e c t t h i s condition and to do so required that the composition of dissolved gases throughout the c i r c u l a t o r y system be c l e a r l y defined. F i n a l l y , the o r i g i n s of bubble growth ( i . e . nucleation s i t e s ) required detailed examination before estimates of i n i t i a l boundary conditions for bubble growth could be established. To date, l i t t l e information i s a v a i l a b l e that describes the s i z e range of nucleation s i t e s found i n physiological systems. An examination of the forms nucleation s i t e s can take, along with physiological geometric constraints, does permit a preliminary estimate of t h e i r s i z e . This i n turn provides i n i t i a l conditions for the solution of the bubble threshold equations. 11 2.1 GBT IN FISH AND OTHER FORMS OF DECOMPRESSION In order to develop a bas is fo r the model development i t i s important to consider the mechanisms by which bubbles form and grow in the c i r c u l a t o r y systems of decompressed or supersaturated animals. Although there are major accumulations of data associated with GBT in f i s h , none of i t provides d e t a i l e d desc r ip t ions of these processes in the c i r c u l a t o r y system. As a r e s u l t there i s l i t t l e that can be used from previous work for comparing t h i s type of bubble formation with that associated with other decompression processes. The physics and physiology of the formation process do however allow c e r t a i n d i s t i n c t i o n s to be made. 2 . 1 . 1 SOURCE AND QUANTITY OF DISSOLVED GASi When comparing GBT with other forms of decompression i t i s the source and quant i ty of the gases cont r ibut ing to bubble growth that provide one of the most important d i s t i n c t i o n s . During both hypobaric decompression (decompression at a l t i tude ) and hyperbaric decompression (decompression from depth) , d isso lved gases cont r ibut ing to bubble growth come only from body f l u i d s and t i s s u e ( H i l l s , 1977). In other words, the quant i t i es of gas involved are l im i ted and f i xed by the mass and l i p i d content of the subject and pre-decompression cond i t ions . Because of the high s o l u b i l i t y of many gases in l i p i d s , they are one of the major sources of d isso lved gas d r i v ing bubble growth. An important feature of hyperbaric and hypobaric decompression i s that with t ime, the normal resp i ra to ry processes reduce the amount of d isso lved gas in the system by the 12 e l iminat ion of gases across the lung sur faces , ( H i l l s , 1977). Thus the actual time of exposure to d isso lved gas tension i s l i m i t e d . In f i s h exposed to supersaturated water the gases promoting bubble growth, rather than o r i g i n a t i n g in the body come d i r e c t l y from the water the f i s h breathes. Consequently, the amount of gas which can contr ibute to bubble growth i s v i r t u a l l y un l imi ted . Furthermore the time periods over which f i s h are exposed to supersaturat ion can be extremely long. In a hatchery or natural water course, salmonids may be in supersaturated water throughout t h e i r e n t i r e juven i le l i f e and during per iods of f resh water migrat ion. Thus, very low l e v e l s of supersaturat ion combined with long per iods of exposure may induce symptoms which would never appear for short per iods of exposure at higher l e v e l s of supersaturat ion . For f i s h exposed to supersaturated water, i n h i b i t i o n of the bubble growth process can come only from changes in environmental parameters such as barometric pressure , hydrostat ic pressure , water temperature or i n t e r a c t i o n of bubble volume with the compliance of the phys io log ica l system in which the bubble i s growing. 2.2 CIRCULATORY SYSTEM BUBBLES IN HYPERBARIC AND HYPOBARIC DECOMPRESSION It has been pointed out that fo r humans and experimental animals exposed to hyperbaric and hypobaric decompression, the gas cont r ibut ing to bubble growth i s that which has been d isso lved in 13 l i p i d s , body - f luids and t i s s u e . As a r e s u l t , t h i s gas general ly comes out o-f s o l u t i o n at the t i s s u e leve l - f i r s t , to -form bubbles which enter the vascular system by inward rupture of small vessels and c a p i l l a r i e s . The 1944 work of Gersh et a l . shows micro-photographs of the rupture process in guinea p igs that have been decompressed from 7 atmospheres to 1 atmosphere. The damaged vessel wal ls are apparent in the photographs and the f ind ing of e p i t h e l i a l c e l l t i s s u e f ree in the blood fur ther supports the f i n d i n g s . The work by P h i l i p et a l . , (1972), provides add i t iona l photographic support in decompressed r a t s , wherein a var ie ty of bubbles and e p i t h e l i a l c e l l t i s s u e are found in the b lood. Under condi t ions of gradual decompression a r t e r i a l blood has reduced d isso lved gas tensions as a r e s u l t of gas unloading at the lungs. In many cases gas which would normally form bubbles in t i s s u e adjacent to a r t e r i a l vesse ls can d i f f u s e in to t h i s blood to r e l i e v e gas tension in the t i s s u e . With the exception of cases invo lv ing rap id decompression, the entrance of gas in to the a r t e r i a l system by vessel rupture may be avoided, ( H i l l s , 1977). Consequently, extravascular bubble formation with subsequent vascular system entry i s usua l l y confined to the venous s ide of the c i r c u l a t o r y system. Another feature of human and mammalian physiology which conf ines bubbles to the venous s ide of the c i r c u l a t o r y system i s the f i l t e r i n g act ion of the lungs combined with stream-wise concentrat ion gradients in the a lveo la r c a p i l l a r i e s . By the time bubbles reach the lungs, they have e i the r grown or coalesced to a s i z e which r e s t r i c t s t h e i r movement through the a lveo la r c a p i l l a r i e s . With the r e l i e f of d isso lved gas tension at the lungs, a stream-wise gradient in d isso lved gas concentrat ion i s estab l ished which al lows bubble gas to return to so lu t ion ( H i l l s , 1977). The cases invo lv ing bubbles in the a r t e r i e s of experimental animals are usua l l y those in which rap id or explosive decompression has occurred, (Gersh et a l . , 1944; P h i l i p et al . . 1972, and H i l l s , 1977). Under these severe condi t ions of decompression, bubbles appear as a r e s u l t of both in t ravascu lar and extravascular bubble formation. 2 .3 CIRCULATORY SYSTEM BUBBLES IN GBT To e s t a b l i s h the d i f f e r i n g modes of bubble formation in GBT i t i s f i r s t necessary to examine how f i s h are exposed to supersaturat ion . This i s important not only from the standpoint of understanding how gases move in to the c i r c u l a t o r y system but a l so in determining i f bubble formation w i l l begin i n t r a v a s c u l a r l y , ex t ravascu lar l y or both s imultaneously . 2 . 3 . 1 EXPOSURE OF FISH TO SUPERSATURATION: F ish can be exposed to supersaturated waters by e s s e n t i a l l y two means. In order to d i s t i n g u i s h between the two, consider f i s h in two containers of i d e n t i c a l water. The f i r s t container i s shal low, whereas the second container has s u f f i c i e n t depth to allow pressure compensation fo r any leve l of supersaturat ion that may be introduced ( i . e . enough depth to prevent bubble growth). See Col t and Cornacchia, (1982) and Weitkamp and Katz , (1980) fo r an explanation of depth or pressure compensation. If now the water in both containers becomes i d e n t i c a l l y supersaturated, perhaps as a r e s u l t of a change in water temperature, f i s h in the f i r s t container w i l l develop in terna l symptoms of GBT determined by the time required for gas to move from the water across the g i l l membrane in to a r t e r i a l blood and then through the c i r c u l a t o r y system to t i s s u e and organs. One would a n t i c i p a t e that the r e s u l t i n g symptoms (bubbles in the b lood, t i s s u e and organs) would develop progress ive ly along the c i r c u l a t o r y paths. Consider next a f i s h in the second container that has remained below the compensation depth. This f i s h w i l l be subjected to the same l e v e l s of d isso lved gas tension with the important d i f fe rence that bubbles w i l l not form. I f , a f te r the b lood , t i s s u e and organs of the f i s h have become thoroughly saturated with d isso lved gases, the f i s h i s moved above the compensation depth to the upper l e v e l s of the container a d i f f e r e n t time course fo r the development of symptoms might be expected. Th is would be the r e s u l t of a l l regions of the body being i n i t i a l l y supersaturated; thereby al lowing the growth of bubbles to begin at a l l l ocat ions s imultaneously . In t h i s form of exposure, a f i s h i s undergoing a type of decompression s i m i l a r to that described above fo r hyperbaric or hypobaric decompression. It should be c lea r that the time to mor ta l i t y fo r the two types of exposure may d i f f e r s u b s t a n t i a l l y due the the progressive development of symptoms in the one case as opposed to the simultaneous development of symptoms in the other case. In terms of bubble growth in the c i r c u l a t o r y system, t h i s d i s t i n c t i o n as to where bubbles f i r s t begin to grow i s important. As has already been painted out , s tud ies of bubble formation in the c i r c u l a t o r y systems of 16 decompressed mammals ind ica te o r i g i n s outs ide the c i r c u l a t o r y system. It i s c lear that in -Fish exposed to shallow water supersaturat ion the progressive d isso lved gas movement through the c i r c u l a t o r y system w i l l lead to bubble formation i n t r a v a s c u l a r l y f i r s t . Extravascular bubble development in deeper t i s s u e w i l l fo l low only l a t e r . In the case of deep water exposure with subsequent movement to the water s u r f a c e , extravascular bubble formation may be occurr ing simultaneously with in t ravascu lar bubble formation. 2 . 3 . 2 ARTERIAL VS. VENOUS BLOODa Bubble formation and growth can occur in both a r t e r i a l and venous blood of f i s h ; however, due to unloading of oxygen to t i s s u e , venous blood has a reduced to ta l gas pressure in comparison to a r t e r i a l blood (Dejours, 1975 and Hoar and Randa l l , 1970). Consequently, the leve l of supersaturat ion required to produce bubbles on both s ides of the c i r c u l a t o r y system must be greater than that required to produce bubbles on the a r t e r i a l s ide a lone. If the degree of supersaturat ion i s great enough and bubbles are f ree to move with the b lood, i t would be ant ic ipated that bubbles could develop to s u f f i c i e n t s i z e by the time they approach the t i s s u e leve l that they are e f f e c t i v e l y blacked from fur ther movement by the small s i z e of t i s s u e c a p i l l a r i e s . This would produce a condi t ion of hemostatis (stoppage of blood flow) which i s considered to be the c r i t i c a l phys io log ica l i n s u l t producing many of the observed m o r t a l i t i e s associated with GBT (Wietkamp and Katz , 19S0). If bubbles form in venous blood as a r e s u l t of very high l e v e l s of 17 supersaturat ion , they should be present throughout the c i r c u l a t o r y system inc lud ing the heart and g i l l s t ruc tu res . Bubbles present in e i ther s ide o-f the c i r c u l a t o r y system and moving with the blood w i l l be blacked e i ther approaching the g i l l s or approaching the t i s s u e and organ c a p i l l a r i e s . If high l e v e l s of supersaturat ion are present and the type of exposure i s f i r s t at depth with subsequent movement to the s u r f a c e , then both in t ravascu lar and extravascular bubble formation may occur. On the other hand i t would be expected that the thresholds fo r bubble formation in t h i s type of exposure w i l l be biased toward in t ravascu lar bubble formation as opposed to extravascular bubble formation. Th is would be the r e s u l t of surface tension being the p r i n c i p a l fo rce involved in bubble growth in the one case , whereas bubble growth in t i s s u e should be i n h i b i t e d by both surface tension and the mechanical strength of extravascular t i s s u e . The important r o l e l i q u i d surface tension plays in bubble formation and growth w i l l be examined in the d iscuss ion of nucleat ion theory l a t e r in t h i s s e c t i o n . A s i m i l a r s i t u a t i o n would be expected for shallow water exposure. Here, extravascular bubble growth would occur only a f t e r bubble growth has reached an advanced stage i n t r a v a s c u l a r l y . The delay would be due in part to the time required to saturate extravascular t i s s u e and in part to the mechanical res is tance that t i s s u e would o f f e r to bubble growth. Again, thresholds should be biased toward in t ravascu lar bubble formation. 18 The point o-f t h i s d iscuss ion has been to es tab l i sh that major d i f fe rences do ex i s t between bubble formation associated with GBT in f i s h and other forms of decompression. In the case of GBT in f i s h , bubble formation and growth i n i t i a l l y occur i n a l i q u i d environment; whereas, in other forms of decompression, bubble formation and growth general ly begins in an extravascular environment. Fur ther , these d i f f e r e n c e s allow mathematical models descr ib ing bubble formation and growth in a l i q u i d to be appropr iate in the one case whereas the other case must account fo r both l i q u i d sur face tension and t i s s u e mechanical p roper t ies . It i s c lear that the d i r e c t i o n of d isso lved gas movement, the quant i t i es of gas cont r ibut ing to bubble growth, the leve l of d isso lved gas tension and period of exposure a re . the important cons iderat ions in d i s t ingu ish ing the var ious forms of decompressi on. 2.4 VASCULAR SYSTEM BUBBLE GASES In order to model bubble growth in the vascular system of f i s h , the gaseous species cont r ibut ing to bubble growth must be accurate ly def ined . The four p r i n c i p a l gases of concern are oxygen, n i t rogen , carbon diox ide and water vapor; however, t h e i r r e l a t i v e cont r ibut ions w i l l vary depending on the locat ion of the bubble. 2 . 4 . 1 NITROGEN: Due to i t s abundance in the environmental water and throughout a l l body compartments of a f i s h , ni t rogen w i l l be the major component of bubble gases in GBT (Harvey,. 1975; Weitkamp 19 and Katz , 19B0 and H i l l s , 1977). Furthermore, nitrogen should be e q u i l i b r a t e d with the environmental water regardless of i t s degree of saturat ion s ince i t i s almost b i o l o g i c a l l y i n a c t i v e . It should a l so be recognized that the s o l u b i l i t y of gases such as nitrogen in l i p i d s i s many times that of nitrogen in water, (Altman and Dittmer, 1971). Thus, i t i s p a r t i c u l a r l y v o l a t i l e in terms of the number of moles of gas re leased from so lu t ion (in l i p i d s ) , per un i t of decompression. This would be p a r t i c u l a r l y important in the cases invo lv ing deep water exposure to supersaturat ion fol lowed by subsequent movement to shallow water. 2 . 4 . 2 OXYGENs Oxygen w i l l provide qu i te d i f f e r e n t cont r ibut ions to bubble growth between the a r t e r i a l and venous s ides of the c i r c u l a t o r y system. Although most oxygen enter ing the blood through the g i l l s i s chemical ly bound to hemoglobin, a r t e r i a l plasma w i l l vary in i t s d isso lved oxygen content (Hoar and Randa l l , 1970). Heming (1984 a ) , f i n d s the p a r t i a l pressure of oxygen in a r t e r i a l blood to be approximately 125 mm. Hg. fo r r e s t i n g Rainbow t rout in normoxic water, (par t ia l pressure of Q z = 150 mm. Hg. ) . This g ives an uptake r a t i o across the g i l l s of approximately 0 .85 . In s l i g h t l y d i f f e r e n t r e s u l t s , Stevens and Randall (1967) report that blood leav ing the g i l l s i s usua l l y 95% saturated with d isso lved oxygen. In s t i l l other s t u d i e s , Randall and Jones (1973) report oxygen a r t e r i a l P o 2 l e v e l s in res t ing Rainbow trout of 59 mmHg. and 73 mmHg. with environmental water P o 2 l e v e l s of 153 mmHg. and 150 mmHg. respec t i ve l y . These r e s u l t s y i e l d uptake r a t i o s of 0.38 and 0 .49. On the venous s ide of the c i r c u l a t o r y system condi t ions are qu i te d i f f e r e n t yet . 20 Due to unloading o-f oxygen to t i s s u e , i t s p a r t i a l pressure in venous blood w i l l be qu i te low - approaching 10 mm. Hg. in t e l e o s t s , (Dejours, 1975). Since oxygen p a r t i a l pressures within the c i r c u l a t o r y systems of f i s h can vary s u b s t a n t i a l l y from that of the environmental water i t i s c lear that the use of water TBP by i t s e l f to evaluate condi t ions fo r bubble growth i s qu i te inadequate and mis leading. It i s important therefore that a bubble growth threshold model inc lude prov is ions to account fo r these v a r i a t i o n s . 2 . 4 . 3 CARBON DIOXIDEs Metabolic C 0 2 i s a major feature of blood acid/base chemistry; however, i t s residence time in the molecular form l i m i t s i t s r o l e in blood bubble growth processes. Although re leased into the blood as molecular C 0 2 from t i s s u e , most of the C 0 2 i s qu ick ly bound to hemoglobin within red blood c e l l s (Hoar and Randa l l , 1984). That which i s not bound in t h i s form i s r a p i d l y converted to bicarbonate within the red blood c e l l and then r e - e n t e r s the plasma through an exchange with ch lo r ide (Hoar and Randa l l , 1984). The erythrocyte i n t r a - c e l l u l a r C 0 2 hydration react ion i s catalyzed by carbonic anhydrase, which produces a react ion hal f time on the order of mi l l i seconds (Hoar and Randal l , 1984). This combined with the high permeabi l i ty of the red c e l l to C 0 2 , s u b s t a n t i a l l y reduces Pco= in the blood. The net r e s u l t i s that the p a r t i a l pressure of C 0 2 in venous blood of Rainbow trout i s about 4 to r r , (Dejours, 1975). Carbon d iox ide on the a r t e r i a l s ide of the c i r c u l a t i o n system e x h i b i t s a p a r t i a l pressure of only two t o r r . , (Dejours, 1975). The lower leve l in a r t e r i a l blood i s due mainly to unloading of C 0 2 at the 21 g i l l s . Because o-f the low l e v e l s o-f carbon diox ide in both a r t e r i a l and venous b lood, i t s cont r ibut ion to vascular bubble growth can be expected to be minimal. 2.4.4 WATER VAPORs Since water i s the major component of b lood, i t s vapor phase w i l l be present in a l l bubbles formed. However, i t s vapor phase w i l l be l imi ted to concentrat ions determined by the vapor pressure at the p r e v a i l i n g temperature. For the purposes of developing a mathematical model fo r c i r c u l a t o r y system bubble growth thresho lds , i t i s c lea r that bubbles formed in the a r t e r i a l s ide of the c i r c u l a t o r y system of f i s h should cons is t p r imar i l y of oxygen, n i t rogen , water vapor and minor amounts of carbon d iox ide . Because of the reduced p a r t i a l pressure of oxygen in the venous s ide of the c i r c u l a t o r y system, bubbles which form and grow in venous blood should cons is t p r imar i l y of nitrogen and water vapor with minor amounts of oxygen and carbon d iox ide . 2 .5 NUCLEATION SITES FOR BUBBLE GROWTH To t h i s point l i t t l e has been sa id regarding the mechanisms by which bubbles grow or from what o r i g i n s they appear. In order to develop a mathematical model descr ib ing threshold cond i t ions , i t i s necessary to e s t a b l i s h the i n i t i a l boundary condi t ions fo r that growth. As with a l l s tud ies invo lv ing time dependent changes of phase, the physics of nucleat ion theory must be considered. 22 This concept w i l l be introduced by f i r s t examining a bubble of gas in a l i q u i d . More s p e c i f i c a l l y , fo r a bubble contain ing one gaseous species in water containing that same species in so lut ion , , the r e l a t i o n s h i p between the pressure of the gaseous species within the bubble and the external water pressure i s given by the Laplace r e l a t i o n s h i p : PF» = Pe + 2o7r (See F renke l , 1935) Eq. 2 .1 where: Pe i s the external water pressure made up of hydrostat ic pressure and atmospheric pressure. 6 is the surface tension of the water. r i s the radius of the bubble. PR i s the bubble in terna l pressure. From the above expression i t can be seen that fo r a given value of Pe, there can be but one bubble rad ius at which equ i l ib r ium w i l l ex i s t between the bubble in terna l pressure and the p a r t i a l pressure of that species in s o l u t i o n . At t h i s r a d i u s , there w i l l be no net t rans fe r of gas between the bubble and l i q u i d . This rad ius however, represents a condi t ion of metastable equ i l ib r ium. For , i f the bubble should gain a molecule of gas from the l i q u i d , the radius w i l l increase and the in terna l pressure w i l l drop - the r e s u l t of the 26/r term decreasing. This w i l l al low add i t iona l gas to move from the l i q u i d to the bubble; thus, i n i t i a t i n g a chain react ion promoting fur ther bubble growth. With no f l u i d motion, the bubble w i l l continue to grow and buoyant fa rces w i l l eventual ly l i f t the bubble to the l i q u i d sur face . In a f lowing 23 system the fa te of the bubble w i l l be determined by the r e l a t i v e magnitudes of the i n e r t i a l , buoyant and drag forces along with the leve l of turbulence in the l i q u i d , ( C l i f t et a l . , 1978). Conversely, i f the bubble should loose a molecule of gas to the l i q u i d , i t s radius w i l l decrease, al lowing the in terna l pressure to r i s e . Here aga in , a chain react ion would promote add i t iona l mass t rans fe r from the bubble to the l i q u i d . In t h i s case the bubble would t h e o r e t i c a l l y co l lapse in to the l i q u i d . It can be seen that as the bubble decreases in r a d i u s , the surface tension component of the bubble in terna l pressure increases . This e f f e c t acce le ra tes the ra te at which the gases are dr iven in to s o l u t i o n . F igure 1. shows the r e l a t i o n s h i p between the d i f fe rence in in terna l pressure , PF» and the external pressure, Pe of a bubble in water as a funct ion of bubble r a d i u s , r. In the general case , PF> would be the sum of the p a r t i a l pressures of a l l gaseous species in the bubble. The metastable radius i s c a l l e d the c r i t i c a l r a d i u s , (Epstein and P l e s s e t , 1950). By the above arguments, i t i s seen that t h e o r e t i c a l l y , bubbles can ex i s t in a l i q u i d on a temporary bas is only . If t h i s were in fac t t r u e , the t e n s i l e strength of water would be on the order of several hundred atmospheres and i t s normal b o i l i n g point would approach 300 degrees C . , (Frenkel , 1950; Fur th , 1941; Dor ing, 1937; F i s h e r , 1948 and F inch , 1969). The reason water does bo i l at a much lower temperature and that bubbles can ex i s t at d isso lved gas tensions of l e s s than one atmosphere i s due to the presence of microscopic gas p a r t i c l e s which have been s t a b i l i z e d 24 within the l i q u i d . These microscopic p a r t i c l e s are c a l l e d heterogeneous nucleat ion s i t e s and are the foundation upon which separat ion of l i q u i d , vapor and gas phases occur within most l i q u i d s , (Dunning, 1969). The nucleat ion s i t e s react to both changes of phase of the l i q u i d and the movement of d isso lved gases in to and out of s o l u t i o n . The mechanisms which permit the s t a b i l i z a t i o n of nucleat ion s i t e s in l i q u i d s have been studied extens ive ly oyer the past several decades and remain an area of current s c i e n t i f i c i n q u i r y , (Pease and B l i n k s , 1947; P l e s s e t , 1969; Herzfeld and Fox, 1954; Hemmingsen, 1970; Harvey et a l . , 1944; Yount, 1983; Yount and L a l l y , 1980; Yount, 1979; Yount, 1981; Yount, 1982 and Yount and Yeung, 1979). From the s tud ies to date three p r i n c i p a l mechanisms have been proposed fo r the s t a b i l i z a t i o n process that would be appropr iate to b i o l o g i c a l systems. In 1944 E. N. Harvey introduced a s t a b i l i t y model which requi res a d i s c o n t i n u i t y in a hydrophobic surface on e i ther the wal ls of the vessel containing the l i q u i d , or on s o l i d p a r t i c l e s suspended within the l i q u i d . The second mechanism, f i r s t introduced by Herzfe ld and Fox (1954), involves the formation of membranes composed of non-so luble organic contaminants around micro-bubbles within the l i q u i d . The t h i r d mechanism involves the juncture of water with a hydrophobic sur face . This mechanism f i r s t proposed by Pease and B l inks (1947) and studied by P lesset (1969) postu lates that in the presence of a hydrophobic su r face , repu ls i ve fo rces between the surface and the l i q u i d w i l l produce weaknesses at the l i qu id/sur face i n t e r f a c e . This in turn al lows 25 reduced l e v e l s o-f d isso lved gas tension to produce a rupture at the i n t e r f a c e in the form of a gas pocket. One of the d i f f i c u l t i e s in applying t h i s l a s t model to supersaturat ion in f i s h i s that i t requi res supersaturated s ta tes on the order of ten atmospheres, (Hemingsen 1970). Although the model may be appropriate in hyperbaric decompression processes; i t i s d i f f i c u l t to see where i t would apply to bubble formation in GBT s ince t h i s involves supersaturated s ta tes of l e s s than two atmospheres. Therefore, in the fo l lowing d i s c u s s i o n , at tent ion w i l l focus on the Harvey and the Herzfeld and Fox models. 2.6 NUCLEATION MODELS Both the Harvey and the Herzfeld and Fox models have the important feature that they provide a means whereby the pressure in a gas nucle i can be maintained lower than the hydrostat ic pressure in the surrounding l i q u i d and thereby prevent the co l lapse of the nuc le i when the l i q u i d becomes undersaturated. Furthermore, both mechanisms have been studied fo r bubble formation in water and to a lesser extent fo r the formation of bubbles in b i o l o g i c a l systems. Each of these mechanisms w i l l be examined in order to extract that information which w i l l be needed for the c i r c u l a t o r y system bubble growth model. 2 . 6 . 1 THE HARVEY MODELS The Harvey model for nuc le i s t a b i l i z a t i o n postu lates that cracks and d i s c o n t i n u i t i e s on hydrophobic surfaces within a l i q u i d cannot be wetted beyond a c r i t i c a l contact angle and must therefore be f i l l e d with a pocket of gas. E s s e n t i a l l y , a 26 balance i s achieved between the fo rces act ing at the l i qu id/gas/so l id surface i n t e r f a c e and the surface tension of the l i q u i d . For nuc le i adhering to a s o l i d su r face , s t a b i l i t y depends on the geometry of the su r face , the shape of the g a s / l i q u i d / s o l i d junc t ion , advancing and receding contact angles between the su r face , l i q u i d and gas as well as sur face tension and the degree of s a t u r a t i o n . The reader should consult both the 1944 and 1951 works of Harvey et a l . fo r a de ta i led descr ip t ion of the nuc le i s t a b i l i z a t i o n mechanism. F igure 3 shows conceptual ly how a nucleat ion s i t e might appear for var ious degrees of supersaturat ion . 2 . 6 . 2 FOX AND HERZFELD MODELS Because of the high surface energy of water, (Adamson, 1967), contaminants are concentrated at any l iqu id/gas in te r face and become even more so during the co l lapse of a bubble. Fox and Herzfeld hypothesized that during the co l lapse of a bubble a point i s reached where the concentrat ion of contaminants i s s u f f i c i e n t to impede fur ther d i f f u s i o n of gases out of the bubble and a condi t ion of s t a b i l i t y i s a t ta ined . Thus, when supersaturat ion i s reintroduced to the l i q u i d , bubble growth begins on these s t a b i l i z e d micronuc le i . Perhaps the most convincing argument fo r the ex istence of nucleat ion s i t e s in b i o l o g i c a l systems s t a b i l i z e d by organic sk ins are the microphotographs of these s i t e s by P h i l p , Inwood and Warren (1972) in the blood of r a t s that had undergone decompression. The organic sk ins can be seen c l e a r l y , (Figures 1 through 6 of the reference) , and e s p e c i a l l y in F igure 3 , where the membrane has been cut with a microtome k n i f e . If the organic sk in form of 27 nucleat ion s i t e s are present in -fish b lood, the bubble growth process may become complicated -further. The sk in may have strength proper t ies which delay bubble growth u n t i l a threshold leve l o-f supersaturat ion i s reached in excess o-f that d ic ta ted by surface tension a lone. 2 . 6 . 3 NUCLEATION SITE SIZEs In e i the r of the above models i t i s necessary to determine the i n i t i a l rad ius of the nucleat ion s i t e from which bubble growth begins. In the mathematical development to fo l low , i n i t i a l boundary condi t ions in terms of rad ius are required to solve the equations fo r threshold values. Unfortunately , there i s no experimental data def in ing the s i z e range of these s i t e s in phys io log ica l systems. There are however, c e r t a i n phys ical and geometrical cons iderat ions which l i m i t the s i z e of nucleat ion s i t e s that can be f ree in the blood. If in the forms of GBT invo lv ing the vascular system the c r i t i c a l phys io log ica l i n s u l t i s the blockage of c i r c u l a t o r y flow by bubbles, then nucleat ion s i t e s , f ree in the blood or attached to the vascular system wa l l s , must be no larger than the diameter of the vesse ls in which they are located . Otherwise, they would block a r t e r i e s and c a p i l l a r i e s even under condi t ions of d isso lved gas equ i l i b r ium. One conclusion which might be drawn therefore i s that the maximum s i z e of in t ravascu lar nucle i f ree in the blood must be on the order of the diameter of erythrocytes which pass through c a p i l l a r i e s . For adult f i s h t h i s ranges from between 1 0 and 3 0 JJM . diameter, depending on the spec ies , (Mott, 1 9 5 7 and Heming, 1 9 8 4 a ) . For very small f i s h such as salmonid a lev ins i t 2 8 i s not known what dimensions would apply . There may be va r ia t ions in the s i z e o-f erythrocytes with the stage of development of the f i s h . Addi t ional research however, would be required to es tab l i sh i f such e x i s t s . For the mathematical development which fo l lows , a mean nuc le i diameter of 20 JJM w i l l be used as a pre l iminary estimate of nucle i diameter and v a r i a t i o n s from t h i s diameter w i l l be examined. 2 . 6 . 4 SURFACE TENSION: Before proceeding with the mathematical development i t should be noted that surface tension fa rces play a cent ra l r o l e in the nuc le i s t a b i l i z a t i o n process (Equation 2 .1 ) . Fur ther , i t i s known that surface tension can vary s i g n i f i c a n t l y depending on the l i q u i d , temperature and, perhaps most important ly , on the presence of surface ac t i ve agents in the l i q u i d , (Adamson, 1967). The surface tension of pure water has been well def ined for decades and i t s surface tension with var ious surface ac t i ve agents has a lso been described ex tens ive l y , (Osipow, 1972). The surface tension of mammalian and e s p e c i a l l y human blood has been studied and defined for normal body temperatures, (Altman and Dittmer, 1961). F igure 2 shows the v a r i a t i o n in surface tension of d i s t i l l e d water as a funct ion of temperature. Also shown on the f i g u r e are the values of surface tension fo r human blood at 37 degrees C e l s i u s . It w i l l be noted that the surface tension of human blood i s c lose to that of water. Unfortunately , f i s h i t s surface tension blood has received l i t t l e at tent ion as p roper t ies ; and, e s p e c i a l l y at the low 29 regards water temperatures encountered by f i s h such as salmonids. The s ing le p iece of work on f i s h blood i s that of Christensen et a l . (1977), for brown trout at 25 degrees C e l s i u s . In t h i s work trout blood surface tension was found to be an order of magnitude l e s s than that of human blood (approximately 5.1 Dynes/cm). Th is e s p e c i a l l y low value i s s u r p r i s i n g s ince order of magnitude changes in the surface tension of water (which i s the major component of blood) requi res the presence of strong su r fac tants , (Osipow,1972). Because of the l imi ted data on i t s value at low temperature an experimental examination of f i s h blood surface tension was conducted as a part of t h i s study. This e f f o r t w i l l be described in the methods and r e s u l t s sect ions to fo l low. 30 3.0 METHODS The d iscuss ions of the previous sect ions estab l ished some of the phys io log ica l and environmental parameters which contro l the formation and growth of bubbles in f i s h exposed to supersaturated water. In t h i s sect ion the bubble growth process w i l l be examined from the standpoint of both the b iophys ica l phenomena involved and the mathematics that allow quant i ta t i ve assessments. 3.1 BUBBLE GROWTH EQUATIONS Much of the o r i g i n a l work involved in the der ivat ion of the phys ica l and mathematical descr ip t ions of bubble growth processes was accomplished at the C a l i f o r n i a Ins t i tu te of Technology, (Zwick and P l e s s e t , 1955; P lesset and Zwick, 1954; Epstein and P l e s s e t , 1950; Zwick, 1954 and Zwick and P l e s s e t , 1955). The essent ia l physics of bubble growth and dynamics were discussed in an exce l lent review paper by P lesset (1964). A thorough treatment of the mathematics i s presented in a paper by Hsieh (1964). In these works the growth and dynamic proper t ies of bubbles are descr ibed in terms of i n e r t i a l , v i scous , heat t r a n s f e r , phase change, mul t ip le species d isso lved gas movement, non-spher ical geometry and non-steady c h a r a c t e r i s t i c s . The complete set of equations cons is t of 16 p a r t i a l d i f f e r e n t i a l equations which, fo r the general case , must be solved simultaneously . Table I presents these equations in vector form for condi t ions of the bubble i n t e r i o r . Equations I through III represent cont inu i t y equations for the gaseous spec ies within the bubb le . . 31 Equation IV i s a momentum equation fo r the system and Equation V i s the energy equat ion. The s t r e s s tensor fo r the system i s def ined by Equation VIII . For the l i q u i d s ide of the bubble a s i m i l a r set of e ight equations apply. The reader should consult P lesset (1964) and Hsieh (1964) for the d e t a i l s of the equation der i va t ions and a p p l i c a t i o n s . The complete set of equations represent a formidable chal lenge for even the most dedicated researcher and consequently are almost never considered in t h e i r complete forms. Solut ions are genera l ly obtained by applying assumptions which s i m p l i f y the mathematics to the point of manageabil i ty . So lut ions have been obtained for s p e c i f i c app l i ca t ions such as changes of phase and the movement of a s i n g l e d isso lved gas species r e l a t i v e to bubbles in a va r ie ty of s o l u t i o n s , (Plesset and Zwick, 1954; P lesset and E p s t e i n , 1950; Zwick, 1954 and Zwick and P l e s s e t , 1955). The s i n g l e gaseous spec ies type of ana l ys i s has been the one most commonly appl ied to problems in hyperbaric and hypobaric decompression (Yang & Lang, 1972). To date these equations have not been appl ied to problems of bubble growth in the c i r c u l a t o r y systems of f i s h exposed to supersaturated water. In order to present the above equations in a clearer form, the bubble growth equations needed fo r t h i s ana l ys i s w i l l be derived for a one dimensional s p h e r i c a l l y symmetric coordinate system. 32 T A B L E I B U B B L E GROWTH E Q U A T I O N S g^-2- + V -<P i V ' i > - 0 Eq. I fj^-3- + V«<e'= V ' 2 > - O Eq. II |E-1 + V <p' V ) - 0 Eq. I l l . + CV'.V >vj - V»T' + p' b Eq. IV . £fjir- + <V • V * )irj +7«h' » T r ( W •?') +g'q' Eq. V where: h' = -A'VT' + | kT'Cn'.V*, + n ' a V ' a - n'V'J n'* n'» n'»n'a(m = - mi) p' V , - V * - - . D ' i a — + - 7 3 1 - Eq. V I n i n a n n £3 p U ' = L T (T',s') Eq. V I I toJ = -p' S J ' + 2>»' ^ € j I - 5 k.1 £ ' J x + B'€ V 6 a 1 Eq. V I I I with € ' J 1 - " ( V ' I . J + V ' j . . ) where: n = ni • n 2 * total number density Pi mini p7 • ni3n2 p = g i + g a y p B g i V , + g 2 V 2 and: b • body force per unit mass B - coefficient of bulk viscosity D 1 2 » coefficient of mass diffusion h » enthalpy k = Boltzman constant m * molecular mass n • number density p = pressure s • entropy T »<temperature t = time U • Internal energy V , V • f l u i d velocity 6 = bubble radius oscillatory amplitude € = pressure f i e l d oscillatory amplitude X • coeff. of thermal conductivity u » coeff. of shear viscosity p = mass density t « stress tensor subscripts and superscripts arei 1 = attached to quantities associated with liquid vapor phase 2 " attached to quantities .associated with dissolved gases ' = quantities associated with bubble interior i,J,k = directions of vector unit normals 33 3 . 1 . 1 ASSUMPTIONS* As with many analyses o-f t h i s type, var ious s i m p l i f y i n g assumptions are required to f a c i l i t a t e the der ivat ion of equations and to obtain s o l u t i o n s . The ana lys i s of t h i s study was developed for a spher ica l bubble in an i n v i s c i d aqueous s o l u t i o n . The ra te of growth (or co l lapse) of the bubble was assumed to proceed s lowly , such that the i n e r t i a l fo rces of the surrounding l i q u i d could be ignored. It was considered that the aqueous so lu t ion contains two a r b i t r a r y gases, A and B, and that the s o l u b i l i t y of these gases in the l i q u i d can be described in terms of Henrys constants . That i s , the d isso lved gas concentrat ions are low and equi l ib r ium concentrat ions can be expressed as a l i n e a r funct ion of pressure. Furthermore, i t was assumed that the temperature dependence of s o l u b i l i t y , although not necessar i l y l i n e a r , i s at l eas t known. See Harvey (1975), F r e i f e l d e r (1982) and B o u t i l i e r e t . a l . (1984) fo r a d iscuss ion of Henrys constant and gas s o l u b i l i t y . Next, i t was assumed that the primary res i s tance to d isso lved gas movement in to and out of so lu t ion l i e s in the l i q u i d phase and i s large in comparison to the res i s tance in the gaseous phase. This al lows the gas phase res i s tance to be ignored in the equation development. The assumption i s one commonly employed in inter—phase mass t rans fe r s tud ies invo lv ing aqueous so lu t ions and atmospheric gases. ,See Welty, Wicks and Wilson (1976) and B i r d , Stewart and L ight foot (1960) for a d iscuss ion of these forms of mass t rans fe r and associated assumptions. 34 3.2 EQUATION DEVELOPMENT With these i n i t i a l assumptions, the - f i rs t step can be taken in developing the appropr iate equations. F i r s t , equations of s ta te are needed for the gases in the bubble or nucleat ion s i t e . Since the gases of concern w i l l u l t imate ly be atmospheric gases at temperatures from 0 to 30 degrees C e l s i u s , the per fect gas law w i l l apply. For the two species A and B the equations w i l l take the forma n « = 4 O r 3 x « PF> / <3 R T) Eq. 3.1 nm - 4 n r 3 x B P P / (3 R T) Eq. 3 .2 where: n i s the number of moles of gas A or B r i s the rad ius of the bubble or nucleat ion s i t e x i s the mole f r a c t i o n of the gas R i s the universal gas constant T i s the absolute temperature of the system By Daltons law the t o t a l pressure of the bubble gases, PF>, w i l l be given by: PF> = P*» + PB + PH2O Eq. 3 .3 where: P* i s the p a r t i a l pressure of gas species A Pa i s the p a r t i a l pressure of gas species B PH2O i s the vapor pressure of water at temperature T 35 And hence, X A = P « / P F > X B = P B / P F > At t h i s point two add i t iona l assumptions are needed. F i r s t i t w i l l be assumed that thermal equ i l ib r ium e x i s t s throughout the bubble/ l iquid system. Second, the water vapor component w i l l be assumed to be in equ i l ib r ium with i t s l i q u i d phase. Equation 3.3 can then be written as : x B = 1 - X A - P H Z O / P P Eq. 3.4 By employing Equation 2.1 in the form: PF> = P E + 26/r Equation 3.4 can be wri t ten as : K B = C P E (1 - X « > - P H S O ] r + 26(1 - x « ) / (P E r+26) Eq. 3 .5 Here, i t has been assumed that surface tension farces are the only surface fo rces a f f e c t i n g bubble growth. In doing so , i t i s recognized that t h i s assumption w i l l lead to minimum threshold condi t ions for bubble growth. If necessary, add i t iona l terms can be included in Equation 3 .5 to account fo r the strength proper t ies of organic sk ins on n u c l e i . 36 Should an ana l ys i s o-f bubble -formation in t i s s u e be requ i red , terms re - f lect ing the mechanical p roper t ies o-f t i s s u e can a lso be included in the equat ion. It should a l so be noted that the term P E i s the sum of a l l external pressures. When bubble growth i s in a f i s h , Pe w i l l inc lude atmospheric pressure , hydrostat ic pressure and the system pressure where the bubble i s growing. That i s , in the case of the c i r c u l a t o r y system P E = Patm. + D h + P B Y S . , where: Patm. = atmospheric pressure p = the densi ty of water h = depth rave. = c i r c u l a t o r y system pressure The subs t i tu t ion of Equation 3 .5 in to Equation 3 .2 r e s u l t s i n : n B = <4nr 3/3RT) CP E(1 - x « ) - P H 2 a + (26/r)( l - x « > 3 Eq. 3 .6 Equations 2.1 and 3.1 can be combined to g ive : n « = ( 4 n r 3 x « / 3 R T ) CP E +(26"/r)J Eq. 3 .7 If Equations 3 .6 and 3 .7 are d i f f e r e n t i a t e d with respect to t ime, t , the fo l lowing r e s u l t s are obtained. 37 drWdt <4n/3RT> C 3 r=CP e ( l - K a ) - PM 2O3 (dr/dt) +46r<l - x « ) ( d r / d t ) - C P E r 3 + 2 6 r = 3 ( d x « / d t ) > Eq. 3 .8 drWdt (4I7/3RT) C ( P E r 3 + 2 6 r = ) ( d x « / d t ) + x « ( 3 P E r = + 46r)(dr/dt)3 Eq. 3 .9 These two equations give the time rate of change of the moles of the two gaseous species in the bubble. This change however must come from d i f f u s i v e or convective exchange of bubble gas with the l i q u i d . The mass movement associated with phase changes has been accounted for in Equations 3 .8 and 3 .9 by the PM=O term and the assumption of phase equ i l ib r ium. The movement of gas across the gas/ l iqu id i n t e r f a c e can be described in terms of the concentrat ion gradients e x i s t i n g at the in te r face and the res i s tance to mass t rans fe r on the l i q u i d s ide of the i n t e r f a c e . For cases where there i s no movement of the i n t e r f a c e and mass t rans fe r i s one dimensional , the basic form of t h i s r e l a t i o n s h i p i s given by the f a m i l i a r F ick r e l a t i o n s h i p : dnx/dt = k A ( d c / d z ) ± (see T reyba l , 1980) Eq. 3.10 where: r t x i s the moles of general gaseous species X k i s a res is tance to mass t ransfer at the in te r face c i s the concentrat ion of the gaseous species z i s a general coordinate which due to spher ica l symmetry w i l l be r in t h i s der i vat ion 38 i i n d i c a t e s , referenced to the i n t e r f a c e A i s the i n t e r f a c i a l area over which mass t ransfer occurs Since i t has been assumed that the p r i n c i p a l res i s tance to mass t rans fe r l i e s in the l i q u i d phase, Equation 3.10 can be wri t ten ass dnx/dt = Hxkt_« A(Pxc - Pxx) Eq. 3.11 where: Hx i s Henrys constant ki_A i s the l i q u i d phase mass t ransfer c o e f f i c i e n t Pxo i s the p a r t i a l pressure of X in the bulk l i q u i d Pxx i s the p a r t i a l pressure of X at the i n t e r f a c e In the above expression i t i s assumed that the p a r t i a l pressures of the bubble gases are in equ i l ib r ium with the gases in so lu t ion at the i n t e r f a c e . This assumption would a lso be v a l i d for the e n t i r e l i q u i d phase at a l l times preceding the instant the bubble begins to grow. The bubble gas pressures may however deviate s u b s t a n t i a l l y from the d isso lved gas pressures in the bulk l i q u i d , once the bubble or nucleat ion s i t e begins to grow. For very slow growth r e s u l t i n g from the gradual imposit ion of supersaturat ion , the p a r t i a l pressures of the bubble gases should stay c lose to the bulk l i q u i d d isso lved gas p a r t i a l pressures. The value of kt_A in the above expression w i l l vary depending on the condi t ions of motion in the l i q u i d r e l a t i v e to the bubble. 39 For stagnant condi t ions the mass t ransfer i s s t r i c t l y by d i f f u s i o n and ki_A takes the form: ki_« = DxL_/r Eq. 3.12 where Dxi_ i s the d i f f u s i v i t y of gas X in the l i q u i d . If there were flow r e l a t i v e to the bubble and the Reynolds number was low, corresponding to Stokes f low, ki_« would take the form: k L A = (Dx L/2r)Cl + (1 + Pf=>E) *' 3 D Eq. 3.13 where: PF-E i s the Peclet Number defined as : P R E = 2rUo/Dxi_ Uo i s the l i q u i d v e l o c i t y r e l a t i v e to the bubble. Interphase mass t rans fe r between bubbles and l i q u i d s has been studied extensive ly fo r a wide var ie ty of flow cond i t ions . As a r e s u l t , expressions fo r kt_A are well def ined for v i r t u a l l y any flow s i t u a t i o n . The reader i s d i rec ted to the work by C l i f f , Grace and Weber (1978) fo r a complete review of the subject . For t h i s der i vat ion i t was assumed that fo r i n i t i a l growth, condi t ions surrounding the bubble are e s s e n t i a l l y quiescent and the form given by Equation 3.12 i s appropriate fo r k i_« . Applying the above equations to the movement of species A and B r e l a t i v e to the bubble in te r face r e s u l t s in the fo l lowing equations. 40 drWdt = 4 H « D « L n r ( P A D - X A C P E + (26/r) 3} Eq. 3.14 dn B/dt = 4 HBD B l _ 1 1 f ( P B O + P H 2 0 CPE + (26/r)3(1 - x A » Eq. 3.15 where P A o and PBO are the p a r t i a l pressures of species A and B r e s p e c t i v e l y , in the bulk l i q u i d surrounding the bubble. Equations 3.8, 3.9, 3 .14 and 3 . 1 5 , under the assumptions s t a t e d , descr ibe the growth of a bubble in an aqueous so lu t ion containing the two d isso lved gases A and B. These equations can be developed fur ther to g ive two d i f f e r e n t i a l equations descr ib ing the bubble growth problem as derived here in . These equations ares dr/dt - RT£H«DAL.CP«O - x A ( P E +(26/r))3 HBDB|_CPBO + P H 2 D — (PE +<26Vr>) (1 - X A ) 33 /C ( P E )r + (46/3)3 Eq. 3.16 dx*/dr • { 0 {CPE (1 - x A ) - Pnao3r + (46/3) (1 - x A ) - uJ x « ( P 6 r + (46/3))} / C(«p + 0 ) (r/3) (P E + (26/r))3 Eq. 3 .17 where: Ijl = HBDBi_CP - (P e + (26/r))(1 - x A )3 X « ( P E + (26/r))3 41 For the steps involved in the development o-f Equations 3.16 and 3.17 from Equations 3 . 8 , 3 . 9 , 3.14 and 3.15 the reader should consult Appendix A of t h i s t h e s i s . In the above express ions, the unknowns r, x A and t are expressed in terms of other quant i t i es which are assumed known for the problem. In genera l , the so lu t ion to these equations requi res a numerical in tegrat ion scheme such as those described in Burden et a l . (1981). The equations as they stand are cor rect however, within the context of the assumptions and can be used to develop threshold c r i t e r i a fo r bubble growth without the need of numerical i n t e g r a t i o n . Before proceeding i t would be appropr iate to f i r s t introduce some conversions of the equations which w i l l make them app l i cab le to var ious regions of the c i r c u l a t o r y system in a f i s h as well as to the environmental water. F i r s t i t i s necessary to convert the a r b i t r a r y gases A and B to s p e c i f i c gases. In the equat ions, A w i l l be changed to "0" and correspond to oxygen, while B w i l l be changed to "N" and apply to n i t rogen. The quant i t i es PNO and Poo are then the p a r t i a l pressures of the d isso lved gases in the bulk l i q u i d in which the bubble i s growing. To convert t h i s condi t ion from the blood to the condi t ions known for the environmental water c e r t a i n other information i s needed. In the pre l iminary cons iderat ions sect ion i t was pointed out that n i t rogen , being metabol ica l l y i n e r t , would be e q u i l i b r a t e d between a l l par ts of the f i s h and the water under steady s ta te cond i t ions . PNO there fo re , can be taken as the water value. It was a lso pointed out that oxygen in a r t e r i a l and 42 venous plasma was not equ i l ib ra ted with that in the environmental water due to the res is tances to mass t ransfer at the g i l l s , unloading of oxygen to t i s sue and the phys io log ica l s ta te of the f i s h . If a new parameter F i s introduced which expresses the r a t i o of plasma O2 p a r t i a l pressure to environmental water O2 p a r t i a l pressure , Equation 3.16 can be writ ten asa dr/dt = R KHoDouCF P ' O A - X o ( P E +(26/r))3 + HlsjDlML- C P ' tMO + P M Z O — ( P E + <26/r))(1 - xa)]} / L I rE — 1 1-1:20 >r +(46/3)3 Eq. 3.18 where primed quant i t i es now ind ica te water values. If the p a r t i a l pressures of d isso lved gases in the water are div ided by the t o t a l pressure of these gases, (defined to inc lude the p a r t i a l pressure of water vapor) , Equation 3.18 can be writ ten ass dr/dt - HoDoi_R "KTGP CF X'o + K ( l - X 'o ) ] - C(xo + K( l - X o ) ) ( P E + (26/r))3> / C ( P E - P M = Q ) r + (46/3))1 Eq. 3.19 where: X ' o i s the r a t i o of the p a r t i a l pressure of oxygen in the environmental water to the to ta l gas pressure (TGP). /HoD TGP = P ' O O + P ' I M O + P H 2 0 43 Likewise, Equation 3.17 becomes: d x « / d r = €CP E ( i — Xo) — P H 2 0 Ir + (46/3)(1 - xo) - Iff X o ( P e r + (46/3) )J / C(l|J + 0) (r/3) (P E + (26/r) )3 Eq. 3 . 2 0 where: iff * - KC(1 - X 'o ) TGP - (Pe + ( 2 6 / r ) ) 3 ( l - x D ) 0' = F X'oTGP - xo(Pe + (26/r)) It should be noted that when examining the growth of bubbles in a r t e r i a l or venous blood the values of Henrys constant and d i f f u s i v i t i e s in Equations 3.19 and 3 . 2 0 must be evaluated for the blood. The above equations can a lso be used fo r examining bubble growth in the environmental water. As already mentioned, t h i s would be appropriate fo r the case where bubbles develop in the buccal cav i t y of small f i s h . The necessary equation can be developed simply by se t t ing F equal to 1 . 0 and evaluat ing the transport parameters ( i . e . d i f f u s i v i t i e s and Henrys constants) fo r the water cond i t ions . The equations can be s i m p l i f i e d fur ther to deal with the case of bubbles growing where just one gaseous species p lus water vapor i s present. As described e a r l i e r , the p a r t i a l pressure of oxygen in venous blood i s low in comparison to that in a r t e r i a l b lood. If i t i s assummed that the oxygen cont r ibut ion to bubble growth i s n e g l i g i b l e then Equation 3 . 2 0 i s not needed s ince Xo and Poo 44 w i l l be zero. Equation 3.19 then s i m p l i f i e s to : dr/dt = R HND CP' N O + P H 2 0 ~~ P E — (26/r)3 /C<PE +P H 2 a ) r + (46/3)3 Eq. 3 .21 Again i t i s necessary to r e l a t e the nitrogen and water vapor p a r t i a l pressures to environmental water condi t ions through the r e l a t i o n s h i p : P ' I M O + P H 2 D + P * O O = TGP From which, P ' N O + P H 2 D = (1 - X'o) TGP Eq. 3 . 2 2 The primed quant i t i es as before r e f e r to condi t ions in the environmental water. The subs t i tu t ion of Equation 3 . 2 2 in to Equation 3.21 r e s u l t s i n : dr/dt. - R HMT D N L C U - X'o)TGP - P E - (26/r)3 / C ( P E +PM5»o)r + (46/3)3 Eq. 3.23 Equations 3 . 1 9 , 3 . 2 0 and 3.23 then comprise the set of equations needed to descr ibe the i n i t i a l stages of bubble growth in the a r t e r i a l and venous s ides of the c i r c u l a t o r y system of a f i s h as well as in the environmental water. The q u a l i f i c a t i o n of i n i t i a l stages of growth i s a consequence of the form of the mass t ransfer c o e f f i c i e n t used in the d e r i v a t i o n . In order to determine thresholds from the above equations i t i s necessary to consider the nucleat ion s i t e s from which bubble growth begins. In applying 45 the equations to the nucleat ion s i t e s , the r term corresponds to the i n i t i a l e f f e c t i v e rad ius of the nucleat ion s i t e , ro . The dr/dt term in the equations then expresses the ra te of change of rad ius with time for the bubble or nucleat ion s i t e . Thus, for s t a b i l i t y dr/dt must be zero , fo r growth dr/dt must be p o s i t i v e and fo r co l lapse dr/dt would be negat ive. Considering the case of growth, the fo l lowing inequa l i t y can be estab l ished from Equation 3.19s TGP CF X ' o + K( l - X 'o )3 - CC(Xo + K( l - Xo)1 C P E + (26/r)3> > 0 Eq. 3.24 Here the the q u a n t i t i e s F X ' o and Xo re fe r to the mole f r a c t i o n s of oxygen in the plasma and the bubble r e s p e c t i v e l y . Before the nucleat ion s i t e s begin to expand in to bubbles, the in te rna l gases w i l l be in equ i l ib r ium with the p a r t i a l pressures of the gases in s o l u t i o n . Thus, xo w i l l be the same as F X ' o and therefore may be replaced by F X ' o . Making t h i s subs t i tu t ion in Equation 3.24 and rearranging i t s form s l i g h t l y , the fo l lowing expression i s obtained for the threshold cond i t ion . T G P A > CF X'od - K) + K] C P E + (26/r) 3 / C X ' o ( F - K) + Kl Eq. 3.25 where the subscr ip t A r e f e r s to a r t e r i a l condi t ions 46 This y i e l d s a general expression fo r bubble growth thresholds in a r t e r i a l blood and r e l a t e s the environmental water to ta l gas pressure to ; 1.) oxygen p a r t i a l pressure r a t i o of the environmental water, 2.) the l i q u i d surface tens ion , 3.) the r a t i o s of the d i f f u s i v i t i e s and Henrys constants fo r oxygen and n i t rogen , 4.) the oxygen uptake r a t i o across the g i l l s and 5.) the pressure in the vascular system which inc ludes atmospheric and hydrostat ic pressures as components. In order to apply the equation to bubble growth in the environmental water, the F term i s set equal to zero and the surface tension i s evaluated for water cond i t ions . For t h i s case Equation 3.25 s i m p l i f i e s t o : TGPew > Pe + <26/r) Eq. 3.26 where the subscr ip t EW r e f e r s to environmental water condi t ions It w i l l be noted that bubble growth threshold c r i t e r i a in the environmental water i s completely independent of the transport parameters in the water. Bubble growth thresholds are dependent only on the densi ty of the water which appears in the hydrostat ic component of the Pe term and the surface tension of water; both of which are well def ined . The only phys io log ica l parameter involved would be the radius of the nucleat ion s i t e . For the case invo lv ing bubble growth in venous b lood, Equation 3.23 can be used to e s t a b l i s h the i n e q u a l i t y : TGPv > CPe + (26/r)D/(l - X'o) 47 Eq. 3.27 where the subscr ipt V r e f e r s to venous blood Here, i t i s seen that threshold c r i t e r i a are again independent of t ransport parameters. The c o n t r o l l i n g parameters are water densi ty and oxygen p a r t i a l pressure r a t i o s coupled with the phys io log ica l parameters of blood pressure , surface tension and nucle i rad ius . 3 .3 EXPERIMENTAL SURFACE TENSION MEASUREMENT In e a r l i e r d iscuss ions i t was estab l ished that the surface tension of f i s h blood i s not known at the low temperatures experienced by f i s h such as salmonids. Furthermore, as shown in the previous mathematical development, bubble growth processes in the c i r c u l a t o r y systems of f i s h exposed to supersaturated water involve surface tension e f f e c t s . In order to support the mathematical model of t h i s t h e s i s i t was necessary to experimental ly evaluate the surface tension of f i s h blood at a reduced temperature. The surface tension of l i q u i d s can be determined by a va r ie ty of methods. Harkins and Alexander (1959) review the var ious techniques in common use and assess t h e i r r e l a t i v e accurac ies . In t h i s study the pendant drop technique was chosen for determining the surface tension of salmonid a r t e r i a l blood at 7 degrees C e l s i u s . This method was chosen because i t permitted a measurement of surface tension a f te r only a few seconds of exposure of the blood to a i r . Other techniques such as that used by Christensen et a K (1977), involve time per iods in excess of f i v e minutes which would allow s i g n i f i c a n t c l o t t i n g to 48 occur before the measurement could be made. In the pendant drop procedure, a drop of blood i s formed at the end of a g lass p i p e t t e . A photograph of the drop y i e l d s var ious dimensional r e l a t i o n s h i p s and through the appropriate equations surface tension i s evaluated. Figure 4 shows a t y p i c a l pendant drop of blood at the end of a p ipe t te . The required dimensions are the maximum diameter of the drop, D E , and the diameter D 8 at a d is tance D E above the vertex of the drop. Surface tension i s then ca lcu la ted from: 6 = gCpb. - p « ) D E 3 F' (See Harkins and Alexander, 1977) Eq. 3.28 where: p b i s the densi ty of f i s h blood p . i s the densi ty of a i r F ' i s a c h a r a c t e r i s t i c shape fac tor fo r the drop The values of F' have been determined experimental ly and are shown in Table IX of Harkins and Alexander. The quant i ty S in the tab le i s the r a t i o D S/D E. Figure 5 shows the experimental apparatus used for forming and photographing the pendant drops of b lood. In t h i s experimental sequence whole blood was obtained from 2 year o ld Rainbow t rou t , Salmo gai rdner i that were cannulated in a method described by Heming (1984 a ) . In t h i s p a r t i c u l a r app l i ca t ion of the technique, Heparin was not used in the cannula in order to avoid any e f f e c t s Heparin may have on sur face tens ion . The f i s h and experimental 49 a p p a r a t u s M e r e m a i n t a i n e d i n a n e n v i r o n m e n t a l c h a m b e r a t a t e m p e r a t u r e o f 7 d e g r e e s C e l s i u s a n d 1 0 0 % r e l a t i v e h u m i d i t y f o r a s i x h o u r p e r i o d b e f o r e b l o o d w a s e x t r a c t e d a n d i n j e c t e d i n t o t h e g l a s s p i p e t t e . T w o f i s h w e r e u s e d i n t h e e x p e r i m e n t s w i t h s e v e r a l b l o o d s a m p l e s t a k e n f r o m e a c h f i s h . T h e t i m e b e t w e e n e x t r a c t i o n o f t h e b l o o d s a m p l e f r o m t h e f i s h a n d p h o t o g r a p h i n g t h e d r o p w a s l e s s t h a n 3 0 s e c o n d s f o r a l l e x p e r i m e n t s . T h e t i m e b e t w e e n e x p o s u r e o f t h e b l o o d t o a i r a n d p h o t o g r a p h i n g t h e d r o p w a s l e s s t h a n 5 s e c o n d s f o r e a c h d r o p . A l l p h o t o g r a p h s w e r e t a k e n w i t h a P e n t a x 3 5 mm c a m e r a u s i n g I I f o r d A S A 1 0 0 f i l m . T h e n e g a t i v e s w e r e m o u n t e d i n s t a n d a r d 3 5 M M s l i d e f r a m e s a n d p r o j e c t e d o n t o a s c r e e n u s i n g a K o d a k 3 5 mm s l i d e p r o j e c t o r . T h e d r o p d i m e n s i o n s w e r e m a g n i f i e d b y a f a c t o r o f a p p r o x i m a t e l y 2 5 u s i n g t h i s p r o c e d u r e . T h i s a l l o w e d a p r e c i s e d e t e r m i n a t i o n o f t h e r e q u i r e d d i m e n s i o n s . N i n e t e e n e x p o s u r e s w e r e t a k e n ; h o w e v e r , o n l y t w e l v e f r a m e s w e r e u s a b l e b e c a u s e m a n y o f t h e d r o p s w e r e n o t c o m p l e t e l y f o r m e d p e n d a n t d r o p s . A p e n d a n t d r o p m u s t h a v e a n e c k e d d o u n s e c t i o n w h e r e t h e d i a m e t e r i s l e s s t h a n i t s m a x i m u m d i a m e t e r ( s e e F i g u r e 4 f o r a n e x a m p l e ) . B l o o d d e n s i t y a s r e q u i r e d i n E q u a t i o n 3 . 2 8 w a s d e t e r m i n e d a s f o l l o w s . W h i l e i n t h e e n v i r o n m e n t a l c h a m b e r t w o 1 . 0 m l s a m p l e s o f b l o o d w e r e t a k e n f r o m e a c h f i s h u s i n g a H a m i l t o n 1 0 0 1 - L T ( 8 1 3 0 1 ) g a s t i g h t c a l i b r a t e d s y r i n g e . T h i s w a s i n j e c t e d i n t o a 1 . 5 m l . v i a l w h i c h h a d b e e n p r e v i o u s l y w e i g h e d o n a S a r t o r i u s 1 6 0 2 M P 8 l a b o r a t o r y s c a l e . T h e v i a l a n d b l o o d s a m p l e w e r e t h e n w e i g h e d a n d d e n s i t y w a s c a l c u l a t e d f r o m t h e w e i g h t d i f f e r e n c e a n d v o l u m e i n f o r m a t i o n . 5 0 I n o r d e r t o c h e c k t h e a c c u r a c y o - f t h e p e n d a n t d r o p t e c h n i q u e a n d t h e d e n s i t y m e a s u r e m e n t s , a s e q u e n c e o f e x p e r i m e n t s u s i n g w a t e r w a s a l s o c o n d u c t e d . S i n c e t h e s u r f a c e t e n s i o n a n d d e n s i t y o f w a t e r a r e w e l l d e f i n e d t h e s e m e a s u r e m e n t s , p r o v i d e d a r e l a t i v e c o m p a r i s o n o f t h e a c c u r a c y o f t h e p e n d a n t d r o p t e c h n i q u e . 5 1 4.0 RESULTS 4.1 THRESHOLD ANALYSIS - ENVIRONMENTAL WATER In order to e s t a b l i s h a bas is fo r comparison, bubble growth thresholds are presented f i r s t fo r environmental water cond i t ions . Using Equation 3 .26 , T6P thresholds are shown in F igure 6 as a funct ion of water temperature fo r sea leve l condi t ions and nucle i r a d i i of 5 , 10, and 20 JJM . . It w i l l be noted that as nuc le i rad ius inc reases , threshold dependence on temperature becomes weaker. This i s a d i r e c t consequence of the r e l a t i v e magnitudes of the 2fi/r term in r e l a t i o n to the Pe term and the dependence of surface tension on temperature (Figure 2 ) . The maximum v a r i a t i o n in TGP threshold i s about 0.003 s t d . atmospheres between a temperature of 0 degrees C. and 20 degrees C. fo r a nuc le i rad ius of 20 juM. F igure 7 shows the same r e l a t i o n s h i p fo r an a l t i t u d e of 700 meters. By comparing the two f i g u r e s i t i s seen that TGP thresholds measured in standard atmospheres decrease with a l t i t u d e . Care should be taken when using t h i s r e s u l t . For example, i f TGP thresholds are expressed in l o c a l atmospheres, the r e s u l t s are as shown in F igure 8 fo r an a l t i t u d e of 700 meters and ind ica tes that threshold l e v e l s increase with a l t i t u d e . Obviously, i t i s important when comparing thresholds at d i f f e r e n t a l t i t u d e s or barometric pressures , that the reference atmosphere be s ta ted . It i s equal ly important to recognize that d i f fe rences in a l t i t u d e are not necessar i l y equivalent to changes in barometric pressure. 52 The theore t i ca l curves of F igures 6 and 7 are based on equi l ib r ium condi t ions at the s p e c i f i e d a l t i t u d e . In other words, a change in a l t i t u d e does not increase or decrease the leve l of supersaturat ion . A l s o , a change in barometric pressure i f i t occurs slowly w i l l not change the leve l of supersaturat ion ; and, under t h i s condi t ion a l t i t u d e and barometric pressure changes are equiva lent . On the other hand, a rap id change in barometric pressure i s a non-equi l ibr ium dynamic e f f e c t that may induce supersaturat ion in to the system. By rearranging Equation 3.26 s l i g h t l y , an expression can be obtained for the depth required to compensate for . a p a r t i c u l a r leve l of supersaturat ion ; that i s , that depth which w i l l prevent bubble growth. The form of the expression i s : He = CPa(TGP*- 1) - (2fi/r)3/73.57 Eq. 4.1 where: Pa = atmospheric pressure in mmHg. TOP' = to ta l gas pressure in atmospheres He = compensation depth in meters Th is r e l a t i o n s h i p i s shown g raph ica l l y i n Figure 9. From the f i gu re i t i s c lear that compensation depth i s a weak funct ion of nuc le i radius fo r large n u c l e i . However, compensation depth shows an increas ing dependence on nucle i radius as radius decreases. As mentioned e a r l i e r in the methods s e c t i o n , bubble growth thresholds fo r the environmental water are independent of oxygen p a r t i a l pressure r a t i o fo r the water. 53 Likewise, as shown in Equation 4 . 1 , compensation depth i s independent of oxygen p a r t i a l pressure r a t i o . 4 .2 THRESHOLD ANALYSIS - ARTERIAL BLOOD Before the threshold equation (Equation 3.25) can be appl ied to bubble growth in the c i r c u l a t o r y system i t i s necessary to e s t a b l i s h the values of the phys ical parameters in the equation. 4 . 2 . 1 SURFACE TENSION: Table II g ives the experimental ly determined values of De, Ds, and the r a t i o Ds/De along with the values of surface tension ca lcu la ted from Equation 3 .28 . Also shown in the tab le are the values of blood and water densi ty which were determined exper imental ly . The values of blood densi ty are s i m i l a r to that of human blood (1.05 gr/mL @ 37 deg. C. - Altman and Dittmer (1961)). For the surface tension c a l c u l a t i o n s water and a i r densi ty are taken from Welty et a l . (1976). Included in the tab les are the mean values for the data s e t s . It w i l l be noted that at 7 degrees Ce ls ius the surface tension of f i s h blood i s only s l i g h t l y lower than that of water. The mean values of the experimental ly determined surface tension of f i s h blood and water are shown in Figure 10 along with the curve of water surface tens ion . Also shown in the f i gu re are the values of surface tension fo r human blood as given in Altman and Dittmer (1961). The c o r r e l a t i o n s ind ica te that the surface tension of Rainbow Trout blood should be qu i te c lose to the experimental ly determined/ va lues . 54 FISH BLOOD SURFACE TENSION CALCULATIONS DENSITY OF FISH BLOOD = 1.0*067 sr/m DENSITY OF UATER = 1.008925 arVmL DENSITY OF AIR 00.1 gr/mL FISH NO. DROP NO. SLIDE NO. Ds/De 1 1 1 1 2 2 2 2 UATER W J n 1 2 3 1 2 3 1 2 3 4 2 5 6 7 9 1 1 13 1* 1 16 18 19 O.6709 O.8719 O. 8668 O. 8738 O. 8705 O. 8795 O. 8809 O. 878 O.859* O.8552 O. 862 O. 8608 BLOOD DENSITY CALCULATIONS SAMPLE NO. UIAL UEISHT 1 2 3 * O. 9921 O. 9775 O. 9909 O. 986 De — cm O. 3875 O. 3831 0. 389* O.3862 O. 3862 O. 3837 O. 3831 O.38** O. * O. 3937 O. O. 3987 O. O. 3906 O. De A2 F De r t2*F#g 150156 O. *52 66.56072 1*6765 O.*5* 65.3*559 151632 O. *61 68.55339 1*9150 O. *51 65.96859 1*9150 O.*57 66.8*622 1*7225 O. *** 6*. 10659 1*6765 O. **3 63. 76233 1*7763 O. **6 6*. 6305* MEAN as STANDARD DEUIA ION = 0. 16 O. *73 7*. 21937 15*999 O. *79 72.81192 158961 O. *68 72.95826 152568 O.*71 70.*7280 MEAN = STANDARD DEVIATION = SISMA 69. 26807 68. 00352 71. 3*180 68. 65187 69. 56519 66. 71*13 66. 35586 67. 25938 68.39*98 1.553525 7*. 88178 73. *6177 73. 609*1 71. 10177 73. 26368 1.36*813 BLOOD + UIAL 2. 0332 2. 0165 2. 029 2. 0305 MEAN = BLOOD DENSITY 1.0*11 1. 039 1. 0381 1.0**5 1. 0*0675 in UATER DENSITY CALCULATIONS SAMPLE NO. UIAL UEI6HT 1 2 3 * O. 989* O. 9858 O. 9855 O. 9877 H20+UIAL 1. 9995 1.9955 1. 9882 2. 0009 H20 DENSITY 1. OlOl 1. 0097 1. 0027 1.0132 MEAN = 1.008925 In the analyses to -follow a mean value of 68.395 dynes/cm. was be used throughout and a l l c a l c u l a t i o n s are fo r a water temperature of 7 degrees C e l s i u s . 4 . 2 . 2 K - TRANSPORT PARAMETERS: Using data from Weiss (1970) fo r 0s and N 2 s o l u b i l i t i e s to c a l c u l a t e Henrys constants and from Perry and Ch i l ton (1973) fo r d i f f u s i v i t i e s of 0s> and N 2 in water, the value of K as a funct ion of temperature i s shown in F igure 11. It w i l l be noted that for the water temperatures shown, the range of K i s f a i r l y narrow. Although the values of Henrys constants increase and d i f f u s i v i t i e s decrease in blood plasma due to the presence of e l e c t r o l y t e s , ( F r e i f e l d e r , 1982 and R a t c l i f f and Ho ldc ro f t , 1963), the r a t i o s of the constants and d i f f u s i v i t i e s are e s s e n t i a l l y the same as that of water. Hence Figure 11 w i l l a l so apply to blood plasma. 4 . 2 . 3 Pe - BUBBLE EXTERNAL PRESSURE: The pressures in the a r t e r i a l s ide of the vascular systems of f i s h can vary both with locat ion and the leve l of a c t i v i t y of the f i s h (Jones and Randa l l , 1978). Although unknown at t h i s time* there may a lso be v a r i a t i o n s with the stage of development of the f i s h . This would depend on a complex r e l a t i o n s h i p between r e l a t i v e va r ia t ions in vascular system dimensions, r e s i s t a n c e , blood volumes, vascular system wall strength and cardiac e f f i c i e n c y . For res t ing adult Rainbow trout Kiceniuk and Jones (1977) show the dorsal aorta d i a s t o l i c pressure to be approximately 25 mmHg. and the s y s t o l i c pressure to be approximately 35 mmHg.. During exerc ise these values can r i s e by three to f i v e mmHg. each. 56 Systemic pressure drops -From the dorsal aorta values to l e v e l s approaching 1 mmHg. on the venous s ide of the system (Jones and Randa l l , 1978). In t h i s ana lys i s the vascular system pressure was taken as that of the environmental water ( i . e a r t e r i a l pressure = 0) fo r most of the cases examined. Thus, the ca lcu la ted thresholds correspond to minimum values and would apply to regions of the a r t e r i a l system approaching t i s s u e c a p i l l i a r i e s . These thresholds may a l so apply to small f i s h such as Salmonid a lev ins and f r y ; however, as mentioned e a r l i e r , the exact r e l a t i o n s h i p between vascular system pressure and stage of development i s not known. The Pe term of Equation 3.25 w i l l then cons is t of atmospheric pressure and hydrostat ic pressure only . 4 . 3 . 4 ARTERIAL BLOOD THRESHOLDS: The s e n s i t i v i t y of bubble growth thresholds in a r t e r i a l blood to var ious b iophys ica l and environmental parameters such as nuc le i r a d i u s , oxygen uptake r a t i o , water oxygen p a r t i a l pressure r a t i o , external pressure condi t ions and water temperature can be examined using Equation 3 .25 . Three values of i n i t i a l nucleat ion s i t e r a d i i were examined for oxygen uptake r a t i o s (F) , of 0 .33 , 0.67 and 0 .85 . Figure 12 shows the theore t i ca l r e s u l t s fo r a r t e r i a l blood at a temperature of 7 deg. C. using the value of f i s h blood surface tension determined e a r l i e r and an F of 0 .33 . F igures 13 and 14 show the same r e s u l t s fa r an F of 0.67 and 0.85 respec t i ve l y . The TGP thresholds are given for a range of X ' 0 from 0.0 to 0 . 5 . For re fe rence , the p a r t i a l pressure r a t i o of 0= in a i r equ i l i b ra ted 7 deg. C. water would normally be c lose to 0 .21 . 57 It should be noted that at an L of 0.0 the values o-f TGP thresholds are the same in a l l three -figures . It i s only at higher values of Xo that the thresholds d i f f e r fo r the three F values. It should a l so be noted that the threshold values at X'o equal to zero correspond to an F of 1.0 fo r a l l values of X'o. This can be seen in Equation 3.25 where fo r an F of 1.0 the X'o terms in the numerator cancel with those in the denominator and y i e l d the same threshold r e l a t i o n s h i p as that of the environmental water - Equation 3.26. F igure 15 shows the v a r i a t i o n of TGP thresholds fo r a r t e r i a l blood at an a l t i t u d e of 700 meters. Again the thresholds are expressed in standard atmospheres. To i l l u s t r a t e the s e n s i t i v i t y of the a r t e r i a l bubble growth thresholds to oxygen uptake r a t i o F, F igure 16 shows t h i s r e l a t i o n s h i p fo r sea leve l cond i t ions , a temperature of 7 degrees Ce ls ius and an environmental water X ' 0 of 0.21. From the f i g u r e , i t i s c l e a r that the oxygen uptake r a t i o i s as important in determining thresholds as the environmental water t o t a l gas pressure. If nuc leat ion s i t e s have a maximum radius of 10 ,uM., corresponding to a c h a r a c t e r i s t i c dimension of f i s h e ry t rocy tes , TGP thresholds can vary by 0.3 atmospheres over an F range of 0.33 to 0.85. For a r t e r i a l b lood, Equation 3.25 can be rewri t ten in a manner as was done for the environmental water to y i e l d the fo l lowing expression fo r compensation depth. 58 H = PaUUVV) - 13 - <267r>>/73.57 Eq. 4.2 where U = TGP'CX*o<F - K) + KD v = F X*o(l - K) + K F igures 17, 18 and 19 show t h i s r e l a t i o n s h i p fo r an X 'o of 0.21 and F values of 0 . 3 3 , 0.67 and 0.85 respec t i ve l y . F i n a l l y , F igure 20 shows the e f f e c t s of an a r t e r i a l pressure of 40 mmHg. on bubble growth thresholds . It w i l l be r e c a l l e d that a l l of the preceeding f i g u r e s are fo r an a r t e r i a l pressure of 0 .0 mmHg.. By comparing the three curves of F igure 20 with those of F igures 12. 13 and 14, i t i s seen that at an X'o of 0.21 the p o s i t i v e a r t e r i a l pressure increases bubble growth threshold by approximately 0.05 s t d . atmospheres at the three values of F. 4 . 2 . 5 VENOUS BLOOD THRESHOLDS: For venous blood where nitrogen and water vapor are the p r i n c i p a l gases involved in bubble growth, a very d i f f e r e n t e f f e c t i s observed in threshold TGP versus water X 'o va lues . F igure 21 show t h i s r e l a t i o n s h i p fo r sea leve l condi t ions and an F value of 0 .85 . Although the values are i d e n t i c a l to those of F igures 12 through 14 at X 'o of zero , the TGP thresholds qu ick ly become much greater than those for a r t e r i a l blood at X 'o greater than 0 . 0 . At X 'o equal to 0.21 and a nucleat ion s i t e rad ius of 10 juM., the TGP threshold fo r venous v blood i s approximately 0 .5 atmospheres greater than that of a r t e r i a l b lood. Thus, as was ind icated e a r l i e r , bubble growth in venous blood requi res s u b s t a n t i a l l y greater t o t a l gas pressures than that required in a r t e r i a l b lood. 59 It i s apparent however, that the leve l i s qui te s e n s i t i v e to the oxygen p a r t i a l pressure r a t i o in the environmental water. 60 5.0 DISCUSSION The bubble growth threshold models and the r e s u l t s o-f t h i s ana lys i s w i l l be discussed in three par ts . The general r e s u l t s in terms of bubble growth thresholds w i l l be examined f i r s t . Next, the e f f e c t s on TGP thresholds of phys ical and phys io log ica l parameters contained in the models w i l l be considered. F i n a l l y , nucleat ion s i t e s w i l l be re-examined to determine t h e i r bearing on the r e s u l t s . 5.1 BUBBLE GROWTH THRESHOLDS 5 . 1 . 1 WATER: By comparing Figure 6 with Figures 12 through 20 i t i s c lea r that TGP thresholds are lower for the environmental water than fo r the c i r c u l a t o r y system of a f i s h . Consequently, fo r the same s i z e nucleat ion s i t e , bubbles w i l l form in the environmental water before forming in the c i r c u l a t o r y system of a f i s h . One symptom of GBT descr ibed in the int roduct ion of t h i s t h e s i s was the development of bubbles in the buccal c a v i t i e s of small f i s h such as salmonid a l e v i n s . These bubbles appear to i n t e r f e r e with r e s p i r a t i o n and lead to su f focat ion in these f i s h . Although the s i z e of nucleat ion s i t e s in the buccal c a v i t i e s of f i s h are not known, t h i s a n a l y s i s suggests that t h i s may be the f i r s t s ign of GBT to appear in young f i s h . This i s p a r t i c u l a r l y t rue s i n c e , un l ike the c i r c u l a t o r y system, there are no apparent geometric l i m i t a t i o n s to the s i z e of nucleat ion s i t e s . The reason that bubble formation in the buccal cav i t y may be a p a r t i c u l a r l y d i f f i c u l t problem for young f i s h i s that small bubbles are 61 inherent ly more s tab le than large bubbles. Surface tension forces i n h i b i t t h e i r deformation or break up into smaller bubbles and buoyant forces are small in r e l a t i o n to the fo rces holding the bubble to a sur face . Compared to large f i s h the s i z e of the buccal cav i t y of a young f i s h would be c loser to the s i z e of these h ighly s t a b i l i z e d bubbles; thus, making i t d i f f i c u l t fo r them to expel the bubble. In larger f i s h bubbles could grow to a s i z e which would allow resp i ra to ry water flow or buoyant forces to s t r i p the bubbles from the surfaces of the buccal cav i t y before they are large enough to i n t e r f e r e with r e s p i r a t i o n . As noted in the r e s u l t s s e c t i o n , bubble growth thresholds in the environmental water are independent of F, the oxygen uptake r a t i o across the g i l l s and X ' o , the water oxygen p a r t i a l pressure r a t i o . Furthermore, thresholds are shown to be a weak funct ion of water temperature except for cases invo lv ing small nucleat ion s i t e s . 5 . 1 . 2 ARTERIAL BLOOD: Bubble growth in a r t e r i a l blood occurs at higher thresholds than those of the environmental water. The thresholds are strong funct ions of both the oxygen uptake r a t i o F, and the water oxygen p a r t i a l pressure r a t i o X 'o . Because f i s h blood surface tension was known only fo r the s i n g l e experimental temperature of 7 degrees C e l s i u s , a l l c i r c u l a t o r y system thresholds were ca lcu la ted fo r t h i s temperature. If the surface tension of f i s h blood var ied with temperature in a manner s i m i l a r to that of water (Figure 2 ) , i t would be ant ic ipated that both a r t e r i a l and venous blood TGP thresholds would d isp lay the same 62 weak dependency on temperature as water. As mentioned above, the exception would be -For small nucleat ion s i t e s (see Figure 6 ) . 5 . 1 . 3 VENOUS BLOODs Comparing F igures 12 through 14 with Figure 20 i t i s c lear that except at X'o = 0 , a r t e r i a l TGP thresholds are s i g n i f i c a n t l y lower than those of venous b lood. Therefore, for the same s i z e nucleat ion s i t e s , bubble growth would appear f i r s t on the a r t e r i a l s ide of the c i r c u l a t o r y system and in venous blood only under condi t ions of very high supersaturat ion . 5.2 PARAMETRIC FORMS 5 . 2 . 1 K - TRANSPORT PARAMETERS: As already noted, i f just one gaseous species i s present in s o l u t i o n , Equation 3.25 can be appl ied by se t t ing Xo equal to 0 .0 and F equal to 1.0. In t h i s case the K term disappears and the TGP threshold becomes a funct ion of surface tens ion , nuc le i rad ius and external pressure only . S i m i l a r l y , in cases invo lv ing the growth of bubbles in the environmental water, F can be set equal to 1.0 and again the thresholds become the same funct ion of surface tens ion , nuc le i rad ius and external pressure. However, for bubble growth in the a r t e r i a l s ide of the vascular system at an F l e s s than one, TGP thresholds now inc lude an add i t iona l dependency on K. This i s the r e s u l t of to ta l d isso lved gas pressure in a r t e r i a l blood being reduced from that of the environmental water. The reduced values are in turn a funct ion of the d isso lved oxygen p a r t i a l pressure r a t i o of the environmental water. The dependency on K r e f l e c t s the f a c t that the r e l a t i v e movement of gases in to and out of 63 so lu t ion ( i . e . nitrogen r e l a t i v e to oxygen) may d i f f e r in the a r t e r i a l blood compared to the r e l a t i v e movement of these gases in a bubble in water. It should be pointed out that t h i s i s an important e f f e c t that appears only fo r a r t e r i a l blood where the oxygen uptake r a t i o i s l e s s than 1.0. It does not appear fo r bubble growth in venous blood or the environmental water. The r e l a t i v e motion of the gases i s an important fac tor not only in es tab l i sh ing thresholds ; but as seen from Equation 2 .23 , w i l l a l so contro l the ra te at which bubbles grow. 5 . 2 . 2 F - OXYGEN UPTAKE RATIOs In examining Figure 17 i t i s apparent that as F decreases, TGP thresholds increase ( i . e . bubble growth i s i n h i b i t e d ) . As described in the pre l iminary cons iderat ions s e c t i o n , values of F from the l i t e r a t u r e vary from about 0.38 to 0 .95. Because of the large v a r i a b i l i t y in observed oxygen uptake r a t i o s , the question a r i s e s as to what the exact phys io log ica l s ta te of the f i s h may have been for these observat ions. Although most of the reported values are supposedly for f i s h at r e s t , i t i s d i f f i c u l t to understand such a wide v a r i a t i o n in t h i s parameter for the same phys io log ica l s t a t e . Since t h i s parameter has a major e f f e c t on TGP thresho lds , i t must be studied more c a r e f u l l y to determine the source of the v a r i a b i l i t y . It should be c lear that s i g n i f i c a n t e r ro rs w i l l ex i s t in the presentat ion of experimental data i f t h i s parameter i s ignored and may be one of the p r i n c i p a l reasons for the great v a r i a b i l i t y that e x i s t s in GBT data as a whole. 64 If the lower F value does indeed r e f l e c t condi t ions fo r a healthy f i s h at rest in normoxic water there should be no reason for the uptake r a t i o to drop below the 0.38 value. It i s known that f i s h regulate oxygen uptake by adjust ing resp i ra to ry volume, resp i ra to ry frequency and heart r a t e , (Randal l , 1970; Dejours, 1975). Through these processes a f i s h can make adjustments to the r a t i o of plasma to water 0=. p a r t i a l pressures. If a f i s h were a c t i v e , metabolic demands would increase and i f not fo r other f a c t o r s , a r t e r i a l p a r t i a l pressures would tend to drop. It i s adjustments to the resp i ra to ry processes as descr ibed above that o f f s e t the tendency toward reduced 0=? p a r t i a l pressure. To f a c i l i t a t e the movement of gas across the g i l l s in these s i t u a t i o n s i t i s suspected that g i l l permeabi l i ty to gas exchange i s increased by the re lease of catecholamines. It has been demonstrated that catecholamines do increase g i l l permeabi l i ty to water movement, ( I sa ia , 1978). Although as yet unproven, i t would n a t u r a l l y fo l low that gas movement might a l so be enhanced. In such a case i t would be expected that the oxygen uptake r a t i o may approach 1.0. It i s noted that due to d i f f u s i v e res i s tance across the g i l l membrane and per fus ive res i s tance at the baso latera l membrane, the value of F can never be equal to 1.0. For condi t ions of both hyperoxia and hypoxia, the data of Randall and Janes (1973) show the uptake r a t i o to be s i m i l a r to that fo r condi t ions of normoxia. For hypoxia ( P o z water = 79 mmHg.) the r a t i o i s 0.38 and for hyperoxia <Po=> water = 416 mmHg.) i t i s 0 .35 . 65 Another -factor which may a-ffeet oxygen uptake r a t i o i s water hardness. Jensen, (1780) found that Steelhead eggs and f r y were l e s s suscept ib le to supersaturat ion in hard water compared to so f t water. Although t h i s may be re la ted to other f a c t o r s , i t i s known that calcium does a l t e r g i l l membrane i o n i c permeabi l i ty ( F r e i f e l d e r , 1982). In doing so i t may a lso a l t e r gas d i f f u s i v e res is tance which in turn w i l l a f f e c t F. However, there i s cur rent l y no data to confirm or re fu te t h i s hypothesis . From Figures 14 through 17 i t i s c lea r that the oxygen uptake r a t i o p lays a c r u c i a l r o l e in es tab l i sh ing TGP thresholds fo r bubble growth. In general i t should be expected that the oxygen uptake r a t i o w i l l be h ighly dependent on the condi t ion of the water and phys io log ica l s ta te of the f i s h . The F fac to r derived in t h i s ana l ys i s has not been considered in any previous s tud ies of supersaturat ion in f i s h . 5 . 2 . 3 X 'o - OXYGEN PARTIAL PRESSURE RATIOs This parameter can vary considerably depending on the source of environmental water. In surface water courses f ree of dams, major f a l l s , rap ids and thermal input , d isso lved gas p a r t i a l pressures w i l l be in equ i l ib r ium with atmospheric a i r and the value of X 'o w i l l be approximately 0 .21 . When dams, f a l l s , rap ids of heating produce condi t ions of supersaturat ion the value of X 'o w i l l vary with d is tance down stream of the source of supersaturat ion . This i s a r e s u l t of general turbulent aerat ion throughout the water course causing d isso lved gas tensions to move toward e q u i l i b r i u m , with the approach to equ i l ib r ium increas ing with d istance downstream of 66 the source o-f supersaturat ion . Due to the d i f fe rence in d i f f u s i v i t i e s of oxygen and nitrogen in water <Perry and C h i l t o n , 1983), oxygen w i l l approach equ i l ib r ium with the atmospheric a i r fas te r than n i t rogen. In such a case i t would be expected that X 'o remains l e s s than 0.21 u n t i l complete equ i l ib r ium i s reached. Well or spr ing water, on the other hand, i s f requent ly low or completely devoid of oxygen while susta in ing high l e v e l s of nitrogen supersaturat ion. The Chi l l iwack and Spius Creek SEP hatcher ies of B r i t i s h Columbia o f f e r examples of t h i s type of water (Shepherd and McDonald 1980). Aerat ion of t h i s water br ings oxygen content to s l i g h t l y below equi l ib r ium condi t ions while nitrogen remains s l i g h t l y supersaturated to produce an oxygen p a r t i a l pressure r a t i o l e s s than 0 .21 . In s i t u a t i o n s where water comes from a large lake , phytoplankton and algae blooms during the warmer months may dr i ve X 'o to values much greater than 0 .21 . fo r par ts of the day (Weitkamp and Katz , 1980). In natural waters, a wide range of water 0s condi t ions are poss ib le and the value of X 'o may vary considerably . However, i n a hatchery environment i t i s u n l i k e l y that water 0= l e v e l s w i l l be fa r from equ i l ib r ium. L ike oxygen uptake r a t i o , the r e s u l t s of t h i s ana l ys i s c l e a r l y show that the oxygen p a r t i a l pressure r a t i o of the environmental water p lays a fundamental r o l e in determining TGP thresholds for bubble growth in the c i r c u l a t o r y systems of f i s h . Again, t h i s 67 parameter has received only limited attention i n the l i t e r a t u r e . Equation 3.25 o-f t h i s analysis provides a clear d e f i n i t i o n of i t s rela t i o n s h i p to other c o n t r o l l i n g parameters. 5.2.4 SURFACE TENSIONS In t h i s derivation, i t was assumed that the only surface force c o n t r o l l i n g bubble growth thresholds was surface tension. That i s , i f organic membranes as described in the preliminary considerations section were present on the nucleation s i t e s , t h e i r strength was n e g l i g i b l e i n r e l a t i o n to surface tension. This of course may not be true; however, there i s currently no information on the strength properties of these membranes. Consequently, the use of surface tension as the only surface force y i e l d s the minimum thresholds for bubble growth. The surface tension of f i s h blood as determined i n t h i s work i s considerably greater than that reported by Christensen §rt a l . (1977). Although the temperature d i f f e r s by approximately 15 degrees C. between the experimental values, i t i s d i f f i c u l t to see why there should be an order of magnitude difference between the two. It i s also d i f f i c u l t to see why the value of Christensen et  a l . should be more than an order of magnitude lower than that of water or human blood (Altman and Dittmer, 1961), considering that water i s the major component of blood. It i s i n t e r e s t i n g to note that Christensen et a l . also measured the density of f i s h blood. Again t h e i r values are an order of magnitude lower than those of t h i s study or the reported values for human blood. This leads one to believe a decimal point i s i n error throughout t h e i r reported data. It should also be noted that i n t h e i r method of determining surface tension, Christensen et a l . allowed the blood samples to 68 set -For f i v e minutes before measurements were taken. In the work of t h i s t h e s i s i t was v i s u a l l y observed that blood c l o t t i n g began within 60 seconds a f t e r exposure to a i r . If i t i s assumed that a decimal point e r ror e x i s t s , the r e s u l t s of Christensen et a l . probably r e f l e c t condi t ions fo r c l o t t i n g blood at room temperature. 5 . 2 . 5 EXPOSURE TO SUPERSATURATION: The question may be asked as to whether the d i f fe rences between the two s ta tes of exposure to supersaturat ion descr ibed e a r l i e r ( i . e . exposure in shallow water versus exposure f i r s t at depth and then movement to the water surface) are important in e s t a b l i s h i n g where bubbles w i l l f i r s t appear in a f i s h . Several s tud ies suggest that the movement of d isso lved .gases through t i s s u e i s qu i te slow and as such w i l l s i g n i f i c a n t l y a f f e c t the time and locat ion of bubble appearance. Yang and Liang (1972), using r a t s , found that the reduct ion in s i z e of subcutaneous pockets of nitrogen gas to one f i f t h t h e i r i n i t i a l volume required 15 days. Although t i s s u e types are d i f f e r e n t from that of f i s h and the transport d i r e c t i o n s are opposite those involved in GBT, the r e s u l t s do i n d i c a t e that the movement of gas through t i s s u e i s a r e l a t i v e l y slow process. In work more d i r e c t l y re la ted to GBT, Harvey (1963) found that Sockeye salmon i n i t i a l l y exposed to water contain ing 14.4 mg./L of d isso lved nitrogen were able to reduce blood nitrogen by 60X within 30 minutes a f te r being placed in water containing 1.6 mg./L of n i t rogen. The r e l a t i o n between blood nitrogen and time did 69 however, exh ib i t an exponential type o-f decay, and the data suggested that a fur ther reduct ion of 20% would requ i re several hours. This was inf luenced no doubt by the slow removal of ni t rogen from t i s s u e . It should a l so be noted that the concentrat ion gradient for the removal of nitrogen (14.1 mg/1 d i f f u s i n g to 1.6 mg/1) was qu i te high and that for problems invo lv ing GBT t y p i c a l concentrat ion gradients are 20.0 mg/1 d i f f u s i n g to 16.0 mg/1. Gorham (1901), by using hydrostat ic pressure compensation, found a l l s igns of GBT (exophthalmia and emboli of the f i n s and head) had disappeared within 24 hours from scu lp in that had been prev ious ly exposed to supersaturated water. Meekin and Turner (1974) found that f i s h s u f f e r i n g from severe symptoms of GBT recovered in a per iod of two weeks a f te r being introduced to equ i l i b ra ted water. The important feature of these var ious s tud ies i s that the movement of gases within a f i s h can be r e l a t i v e l y slow depending on the region being considered and l o c a l concentrat ion grad ients . It should be c lea r therefore that the type of exposure to supersaturat ion w i l l p lay a v i t a l r o l e in e s t a b l i s h i n g which symptoms of GBT w i l l f i r s t appear and which forms of phys io log ica l i n s u l t w i l l u l t imate ly lead to mor ta l i t y . 5 .3 NUCLEATION SITES, FREE OR FIXED The r e s u l t s of the threshold ana lys i s have been shown for mean nucleat ion s i t e r a d i i of 5 , 10 and 20 j i M . This was based on the c r i t e r i a that nuc le i f ree in the blood must i n i t i a l l y be no larger 70 than the s i z e of f i s h blood erythrocytes that pass through g i l l and t i s s u e c a p i l l a r i e s . It i s important to .cons ider that nucleat ion s i t e s may not be f ree in the blood and therefore may be of greater rad ius than that d ic ta ted by the s i z e of erythrocytes . If t h i s i s t r u e , then bubble growth may occur at much lower T6P thresholds than ind icated in F igures 9 through 21. In order to examine t h i s p o s s i b i l i t y c l o s e r , one must reconsider the nucleat ion models described e a r l i e r and var ious p ieces of experimental informat ion. A d i f f i c u l t y e x i s t s in reso lv ing the Harvey hydrophobic surface d i scont inu i t y model and the Fox -Herzfeld organic skin models with the a b i l i t y of var ious inves t igators to form bubbles an nucle i in bulk l i q u i d as apposed to nuc le i on the wal ls of the containing v e s s e l . In p a r t i c u l a r , the question i s ra ised in the case of the c i r c u l a t o r y system as to whether there are nucleat ion s i t e s f ree in the b lood, attached to the vessel wa l l s , or both. The fac t that bubbles do appear in the c i r c u l a t o r y systems of f i s h at moderate l e v e l s of supersaturat ion has been well documented in the l i t e r a t u r e , (See the review works already mentioned). Therefore, nucleat ion s i t e s of some form must ex i s t in the c i r c u l a t o r y systems of f i s h . In experiments using decompressed animals , Harvey e t . a l . (1944), reported that i t was impossible to induce bubble formation within the blood; and yet , bubbles would develop r e a d i l y on vascular system wal ls . This would imply the absence of large nucleat ion s i t e s f ree in the blood and impl icates the vessel wal ls as the source of the larger nucleat ion s i t e s . S i m i l a r l y , Pease and B l i n k s , (1947) found i t impassible to form bubbles in bulk water at l e v e l s of supersaturat ion normally encountered in decompression processes. 71 Yet , as described in the int roduct ion Ph i lp et a l . (1972), -Found what appear to be nucleat ion s i t e s with a -form of organic skin •free in the blood of decompressed r a t s . It i s important that these d i f f e r i n g observations be reso lved ; f o r , i t w i l l have a major bearing on the thresholds at which bubble growth can occur. If in the forms of GBT invo lv ing the vascular system the c r i t i c a l phys io log ica l i n s u l t i s the blockage of c i r c u l a t o r y flow by bubbles, i t i s important whether the bubbles grow from nucleat ion s i t e s on the vascular system wal ls at the point of blockage or are c a r r i e d to that locat ion by the blood. This becomes c leare r when the fo l lowing dimensional considerat ions are examined. If bubbles do form on vascular system wa l l s , there i s no evidence to suggest that they would form p r e f e r e n t i a l l y at one locat ion as apposed to another - i . e . c a p i l l a r i e s versus large a r t e r i e s . Again, one might e a s i l y conclude that the maximum s i z e of in t ravascu lar nuc le i must be on the order of or l e s s than the diameter of the erythrocytes which pass through c a p i l l a r i e s . As noted e a r l i e r , t h i s ranges from between 10 and 30 juM. diameter fo r adult f i s h , depending on spec ies , ( l iott, 1957 and Hemming, 1984). And aga in , fo r very small f i s h such as salmon a lev ins i t i s not known what dimensions would apply. If one examines the dimensional range of vessels within the vascular system of a f i s h and the corresponding th ickness of the vessel wa l l s , other hypotheses are p o s s i b l e . Considering r e l a t i v e as well as absolute dimensions, one would a n t i c i p a t e that the chances of f i nd ing a 10 JJM . diameter d i s c o n t i n u i t y or nucleat ion s i t e in the wal ls of an in tac t 20 JJM . diameter c a p i l l a r y would be smal l . Here the in tac t 72 q u a l i f i c a t i o n excludes c a p i l l a r i e s that have been damaged. Oh the other hand, the chances of f ind ing a nucleat ion s i t e of t h i s s i z e in the wal ls of a 200 ,uM. diameter ar tery should be considerably greater . Furthermore, i t would be ant ic ipated that a very large ar tery could support many nucleat ion s i t e s of 10 uM diameter or l a rge r . It would fo l low there fore , that there may be a r e l a t i o n s h i p between the maximum s i z e and number of nucleat ion s i t e s attached to a vessel wall and the diameter of the v e s s e l . If t h i s i s indeed t r u e , then bubble growth in larger vessels could occur at much lower values of d isso lved gas tens ion . As suggested e a r l i e r , there may be va r ia t ions in the s i z e of c a p i l l a r i e s between adult and small f i s h . It would be expected that these va r ia t ions are small in r e l a t i o n to the va r ia t ions in s i z e of major a r t e r i e s between large and small f i s h . For example, main a r t e r i e s in salmonid a lev ins and f r y may be smaller than the same a r t e r i e s in an adult f i s h by more than an order of magnitude. If there i s a r e l a t i o n s h i p between the s i z e of nucleat ion s i t e s and the s i z e of v e s s e l s , i t would fo l low that bubble growth in small f i s h may requi re higher l e v e l s of d isso lved gas tension than that required fo r large f i s h . There remains the inconsistency regarding the a b i l i t y of var ious researchers to f i n d nucleat ion s i t e s f ree in blood or other f l u i d s as opposed to nucleat ion s i t e s f i xed on the wal ls of the containing vesse l s . This may be resolved by examining more recent information on the s i z e of nucleat ion s i t e s in aqueous so lu t ions . Yount and co-workers (Yount, 1983; Yount and L a l l y , 1980; Yount, 1979; Yount, 1981; Yount, 1982 and Yount and Yeung, 1979), have 73 examined nucleat ion s i t e s in bulk water with emphasis on es tab l i sh ing decompression schedules -for d i ve rs . Using g e l a t i n as a bubble growing medium, good experimental c o r r e l a t i o n was obtained between the s i z e of nucleat ion s i t e s back ca lcu la ted from observed bubble s i z e s and the s i z e of f i l t e r s through which the water was o r i g i n a l l y passed. One of the observations obtained in these s tud ies i s that the s i z e of the nucleat ion s i t e s found in water are too small ( i . e . l e s s than 1.0 juM.) to account for bubble growth at the low l e v e l s of supersaturat ion commonly encountered in GBT . This i s consistent with e a r l i e r work by Liebermann, (1957) who found nuc le i f ree in pure water were genera l ly l e s s than 1. juM. in diameter. On the other hand, P h i l i p e t . a l . (1974), found nucleat ion s i t e s in the blood of decompressed r a t s to be on the order of 10 >iM. in diameter. It should be noted in Figure 1. that nucleat ion s i t e s on the order of 10 pM. rad ius are consistent with the l e v e l s of supersaturat ion commonly observed in problems of GBT. The d i f fe rence between the observat ions by Yount et a l . (1980) and those of P h i l i p et a l . (1974) may be re la ted to an important d i f fe rence between the sequence of decompression and the s ta te of the samples examined. In Younts s tud ies the growth of bubbles was e s s e n t i a l l y under condi t ions of constant supersaturat ion . In the experiments with rat blood by Phi lp et  a l . t the blood had undergone decompression and then r e - e q u i l i b r a t e d with the ambient environment. The two theor ies of nucleat ion and the above experimental observations can be resolved i f one accepts the hypothesis that nucleat ion s i t e s are i n i t i a l l y present both on the wal ls of the vesse ls and f ree in the l i q u i d . Before any decompression has occurred the nucleat ion s i t e s f ree in 74 the l i q u i d are qui te small and requi re large l e v e l s o-f d isso lved gas tension to ac t i va te them. This would be consistent with the observations of Liebermann, (1957) and Yount for water where nuc le i r a d i i are genera l ly l e s s than 1.0juM.. On the other hand, i f the above desc r ip t ions ho ld , nucleat ion s i t e s present on the wal ls of the vessel can be act ivated into growth at much lower l e v e l s of supersaturat ion . This would be consistent with the observations of Harvey and others in that they could induce bubble formation on the wal ls of vessels and not in the blood. If a f te r bubbles have been formed on the wal ls of the vessel and subsequently re leased in to the b lood , the degree of supersaturat ion i s re laxed , these bubbles w i l l begin to co l lapse and in the process may develop the organic sk ins observed by Ph i lps and co-workers. The sk ins would eventual ly retard and s t a b i l i z e the co l lapse process as hypothesized by Fox and Her t z fe ld . These bubbles could then become new f ree nucleat ion s i t e s s u b s t a n t i a l l y larger than the ones from which they o r i g i n a l l y developed. The var ious experimental observat ions may thus be resolved with the theor ies examined here i f both theor ies are accepted and integrated in terms of the h i s to ry of exposure to condi t ions of supersaturat ion . The important considerat ion in terms of GBT in f i s h i s the e f f e c t of previous bubble formation on subsequent exposures to supersaturat ion . If a previous episode of GBT has occurred that was not severe enough to be l e t h a l , but yet allowed bubble formation to occur in the b lood, the next app l i ca t ion of supersaturat ion may i n i t i a t e bubble growth on nucleat ion s i t e s which are larger and therefore can be act ivated at lower l e v e l s of supersaturat ion . Since l i t t l e i s known about 75 the i n i t i a l s i z e o-f nucleat ion s i t e s e x i s t i n g in or on the wal ls of the c i r c u l a t o r y system, the above d iscuss ion serves mainly to point out that vascular bubble formation cannot be ru led out at l e v e l s of supersaturat ion lower than those shown in F igures 12 through 20. If nuc leat ion s i t e s are 100>uM. or more in diameter, TGP thresholds may be on the order of 1.03 atmospheres which as noted in the int roduct ion of t h i s t h e s i s corresponds to observed morta l i ty thresholds . Thresholds of t h i s leve l would a lso correspond c l o s e l y to those associated with swim bladder o v e r i n f l a t i o n ( F i d l e r , 1984) and i t might be d i f f i c u l t to d i s t i n g u i s h between the two except perhaps in terms of time to mor ta l i t y . An exception could involve small f i s h where vascular dimensions may l i m i t the s i z e of nucleat ion s i t e s and l e v e l s of d isso lved gas tension required fo r bubble growth. The other value to the above d iscuss ion i s to show that there can be consistency in the two theor ies of nucleat ion which have been examined and the experimental observations of var ious researchers . 5.4 CONCLUSION The r e s u l t s of t h i s study have provided the f i r s t b iophys ica l mathematical desc r ip t ion of bubble growth thresholds in the c i r c u l a t o r y systems of f i s h . The model c l e a r l y shows the r e l a t i o n s h i p between many important parameters that have not been accounted for in previous work. Two of these parameters, oxygen uptake r a t i o and environmental water p a r t i a l pressure r a t i o , are as important in es tab l i sh ing threshold condi t ions as environmental water t o t a l gas pressure. In a d d i t i o n , the study has provided 76 information on the surface tension of f i s h blood at 7 degrees C e l s i u s . The experimental ly determined value shows that the surface tension of f i s h blood i s s l i g h t l y reduced from that of water. This information along with other phys io log ica l and physical parameters which can be determined e a s i l y leave threshold nucleat ion s i t e s i z e as the only unknown parameter that must be estab l ished before the model can be appl ied more p r e c i s e l y . Once nucleat ion s i t e s i z e i s determined, the model can be used to perform more de ta i led examinations of the s e n s i t i v i t y of GBT thresholds to environmental and phys io log ica l parameters. The s i z e of c r i t i c a l nucleat ion s i t e s ( i . e . those that are act ivated at the lowest TGP thresholds) can be estab l ished through any one of several experimental procedures. For example, the model developed in t h i s study descr ibes threshold fo r bubble growth. Above the threshold TGP, bubbles grow and below the threshold TGP they are e i ther s tab le or c o l l a p s e . If bubbles do grow, they w i l l a l t e r c i r c u l a t o r y system pressure due to the added volume of the bubbles. By monitoring c i r c u l a t o r y system pressure under cont ro l led incremental app l i ca t ions of supersaturat ion , one can then back c a l c u l a t e from Equation 3.25 the e f f e c t i v e nucleat ion s i t e rad ius . An a l t e r n a t i v e or complementary approach would be to open the a r t e r i a l s ide of the vascular system and examine the blood for the presence of bubbles again under condi t ions of incremental app l i ca t ions of supersaturat ion . In e i ther approach i t would be c r u c i a l to monitor a r t e r i a l oxygen p a r t i a l pressure in order to e s t a b l i s h the oxygen uptake r a t i o F. It should be pointed out that because the model i s a threshold 77 model i t does not provide any information on the time course to mortality. To e s t a b l i s h t h i s r e l a t i o n s h i p , Equations 3.16 and 3.17 would have to be integrated and coupled with the compliance properties o-f the vascular system. An equally important consideration i s that under many conditions o-f exposure, the degree of supersaturation may vary during the period of exposure leading to highly non-steady conditions. Again t h i s would have to be included in the integration of the bubble growth equations and vascular system compliance properties. 78 6.0 REFERENCES Ack les ,K . N.5 1973. Proc. Symp. on Blood-bubble Interact ion in Decompression S ickness , Canadian DC I EM Conf. Proc> 73-CP-960. Cand. De-fence Research Board, Downs vi l i e , Ont. Adamson, A. W.; 1967. Physical Chemistry of Surfaces; Academic Press . New York A lderd ice , D.; Jensen, J . 0. T. and Schnute, J .s 1985. An assessment of the inf luence of a n c i l l a r y f a c t o r s on the responce of salmonids to t o t a l gas pressure. Department of F i s h e r i e s and Oceans, Canada, P a c i f i c B i o l o g i c a l S tat ion (In preparation) Altman, P .L . and Dittmer, D.S. 1961. Blood and Other Body F l u i d s . Federation of American S o c i e t i e s fo r Experimental Bio logy . Altman, P .L . and Dittmer, D.S. 1971. Respi rat ion and C i r c u l a t i o n . Federation of American S o c i e t i e s fo r Experimental Bio logy . Becker, C. 1973 Columbia River Thermal E f f e c t s Study: Reactor E f f luent Problems. J . Water P o l l . Control Fed. 45:850-869. Beiningen, K.T. and E b e l , W.J. 1970. E f f e c t of John Day Dam on d isso lved nitrogen concentrat ions and salmon in the Columbia R iver , 1968. Trans. Am. F i s h . Soc. 99:664-671 Beiningen, K.T. and E b e l , W.J. 1971. Supersaturation of d isso lved nitrogen in the Columbia and lower Snake R ivers , 1965-69. U.S. Dept. Commer., N a t l . Mar. F i s h . S e r v . , Data Report 56. 79 Bennett, P. B. and E l l i o t t , D. H.: 1969. The Physiology and Medicine o-f Diving and Compressed A i r Work. B a i l l i e r e , T i n d a l l and Cassel, London Bird, R. B.; Stewart, W. E. and Light-foot, E. N.: 1960. Transport Phenomena. John Wiley & Sans, New York Blahm, T. H.; McConnell, R.J. and Snyder, G.R. 1975. Ef f e c t s of gas supersaturated Columbia River water on the survival of juvenile Chinook and Coho salmon. NOAA Technical Report NMFS SSRF 688. Bonin, B.s Straub, P. W.s S c h i b l i , R. and Buhlmann, A. A.s 1973. Blood coagulation during c r i t i c a l decompression following diving experiments with oxygen/helium; Aerospace Medicine, 44 Bouck, G.R.; Chapman, G.A.; Schneider, P.W. J r . and Stevens, D.G. 1970. Observations of gas bubble disease i n adult Columbia River Sockeye salmon. P a c i f i c Northwest Laboratory, Federal Water Quality Administration, C o r v a l l i s , Oregon. Bouck, G.R. 1984. Bonneville Power Administration, Di v i s i o n of Fish and W i l d l i f e , Portland Oregon (Personal comunication). B o u t i l i e r , R.G.; Heming, T.A. and Iwama, G . K . : 1984. Physicochemical parameters for use in f i s h respiratory physiology. In Fish Physiology, Vol. Xa. Edited by W.S. Hoar and D.J. Randall, Academic Press Burden, R. L.; Faires, J. D. and Reynolds, C. A.s 1981. Numerical Analysis. 2nd.ed. Pr i n d e l , Weber and Schmidt, Boston C a s i l l a s , E.; M i l l e r , S. E.; Smith, L. S. and D'Aoust, B. G.s 1975. Changes i n hemostatic parameters i n f i s h following rapid decompression. Undersea Biomedical Research. 2 80 C a s i l l a s , E . ; Smith, L. S. and D'Aoust, B. S.s 1976. The response o-f f i s h blood c e l l s , p a r t i c u l a r l y thrombcytes, to decompression. Undersea Biomedical Research. 3 Chr is tensen, G. M.s F iandt , J . T. and Poeschl , B. A.s 1977. C e l l s , p r o t e i n s and ce r ta in phys ica l -chemical p roper t ies of brook trout b lood. U.S.A. Environmental Protect ion Agency, Duluth, Minn. C l i f t , R.; Grace, J . R. and Weber, M. E.s 1978. Bubbles, Drops and P a r t i c l e s . Academic Press , New York C o l t , J . E. and Cornacchia, J . W. s 1982. The e f f e c t s of d isso lved gas supersaturat ion on l a r v a l s t r iped bass. Dept. of C i v i l E n g . , Un ivers i t y of C a l i f o r n i a , Davis , C a l i f . Coutant, C. C. and Genoway, R. G.s 1968. F ina l report on an exploratory study of i n te rac t ion of increased temperature and nitrogen supersaturat ion on morta l i t y of adult salmonids. A report to the United States Bureau of Commercial F i s h e r i e s , S e a t t l e , Wash. Davson, H.s 1964. A Textbook of General Physiology. 3rd . ed. C h u r c h i l l , London Dawley, E. M.; Schiewe, M. and Monk, B.s 1976. E f f e c t s of long term exposure to supersaturat ion of d isso lved atmospheric gases on juven i le Chinook salmon and Steelhead t rout in deep and shallow tank t e s t s . ; Gas Bubble Disease. CONF-41033, Tech. Infor . Center , Energy Research and Development Admin. , Oak Ridge Tenn. U.S.A. Dejours, P; 1975. P r i n c i p l e s of Comparative Physiology; North Holland/American E l s e v i e r ; New York Dor ing, W.s1937. Die Uberhitzungsgrrnze und Z e r r e i s s f e s t i g k e i t von F l u s s i g k e i t e n , Z. Phys. Chem., Vol B36 81 Dunning, W. J . : 1969. General and theore t i ca l in t roduct ion . Ins Nucleat ion. Ed. by A. C. Zettlemoyer. , New York E b e l , W. J . ; Kroma, R.W. and Raymond, H.L. 1973. Evaluat ion o-f F ish Protect ion F a c i l i t i e s at L i t t l e Goose Dam and review o-f other s tud ies r e l a t i n g to protect ion o-f j uven i le salmonids in the Columbia and Snake R ivers , 1973. National Marine F i s h e r i e s Se rv i ce , Northwest F i s h e r i e s Center , S e a t t l e , Washington. E b e l , W.J. 1979. E-f-fects o-f atmospheric gas supersaturat ion on surv i va l of f i s h and evaluat ion of proposed so lu t ions . In United States Army Corps of Engineers. F i f t h progress report on f i s h e r i e s engineering research program 1973-1978. Port land D i s t r i c t , F ish and W i l d l i f e Sec t ion , Port land Oregon. Ecker t , R. and Randal, D.s 1983. Animal Physiology. W. H. Freeman & C o . , San Francisco Eps te in , P. S. and P l e s s e t , M. S . : 1950. On the s t a b i l i t y of gas bubbles in l i q u i d - g a s s o l u t i o n s . The journal of Chemical Phys ics , Vo l . 18, No. 11 F i d l e r , L. E . , : 1983. A proposal fo r the study of b iophys ica l phenomena associated with gas bubble trauma in f i s h . To the Department of F i s h e r i e s and Oceans, Salmonid Enhancement Program Penny Appl ied Sc iences , L td . F i n c h , R. D.s 1969. Hole Theory of Cav i ta t ion Nucleat ion. Physics of F l u i d s , Vo l . 12 No. 9 F i s h e r , J . C.s 1948. The Fracture of L iqu ids . J . Appl . Phys ics . Vo l . 19 82 Fax, F. E. and Herzfeld, K. F.: 1954. Gas bubbles with organic skin as c a v i t a t i o n n u c l e i . The Journal of the Acoustical Society of America. Vol. 26, No. 6 F r e i f e l d e r , D.: 1982. Physical Chemistry for Students of Biology and Chemistry. Science Books I n t l . Boston Frenkel, J.s 1955. Kinetic Theory of Liquids, Dover Furth, R.: 1941. On the Theory of the Liquid State. Proc. of the Cambridge Philosophical Soc. Vol. 37 Gersh, I.; Hawkinson, G. E. and Rathbun, E.N.s 1944. Tissue and vascular bubbles aft e r decompression from high pressure atmospheres - c o r r e l a t i o n of s p e c i f i c gravity with morphological changes. Journal of C e l l u l a r and Comparative Physiology, Volume 24, 1944 Harding, D.R.: 1984. SEP Support B i o l o g i s t , Lower Mainland, Department of F i s h e r i e s and Oceans; May 1984. (Personal communication). Harkins, W. D. and Alexander, A. E. in Physical Methods of Organic Chemistry, Weissberger, E. Editor, 3rd. Ed. Interscience Harvey, E.N.; Barnes, D.K.; McElroy, W.D.; Whiteley, A.H.; Pease, D. C. and Cooper, K.W.s 1944. Bubble formation i n animals. Journal of C e l l u l a r and Comparative Physiology, Volume 24, 1944 Harvey, E. N.; McElroy, W.D.; Whiteley, A.H.; Warren, G.H. and Pease, D.C.: 1944. Bubble formation i n animals. Journal of C e l l u l a r and Comparative Physiology, Volume 24, 1944 83 Harvey, E. N. : 1951. Physical f a c t o r s in bubble formation. In: Decompression Sickness. Ed. by J . F. Fu l ton . Saunders, Ph i lade lph ia Harvey, H.H. 1963. Pressure in the ear l y l i f e of Salmon. Ph.D t h e s i s , Un ivers i ty of B r i t i s h Columbia. Harvey, H.H. 1975. Gas disease in f i s h - a review. In Chemistry and physics of aqueous s o l u t i o n s . W.A. Adams, E d i t o r . The Electrochemical Soc ie ty , P r inceton , New Jersey Heming, T. A . : 1984 a . Unpublished Data. Dept. of Zoology, Un ivers i ty of B r i t i s h Columbia, Vancouver, B. C. Heming, T. A . : 1984 b. The r o l e of f i s h erythrocytes in t ransport and excret ion of carbon d iox ide . Ph.D. Thes is , Un ivers i ty of B r i t i s h Columbia. Hemmingsen, E. A . : 1970. Supersaturation of gases in water: Absences of c a v i t a t i o n on decompression from high pressures. Sc ience, 167 Hempleman, H. V . : 1975. Present s ta te of the a r t . In: Proc. Workshop on Decompression Procedures fo r depths in Excess of 400 F t . Ed. by Ii. Beckett , UMS, Washington H i l l s , B. A . ; 1977. Decompression Sickness; John Wiley & Sons; New York Hoar, W. S. and Randal l , D. J . : 1970. Eds. of F i sh Physiology, V o l . IV. , Academic Press , New York 84 Hoar, W. S. and Randal l , D. J . : 1984. Eds. of F ish Physiology, Vo l . X . , Academic Press , New York Hol land, J . A.s 1969. Discussion of dessiminated in t ravascu lar coagulat ion in decompression s ickness . Report 585, U.S. Naval Sub. lied. Center, Groton, Conn. Hsieh, D. Y.e 1965. Some a n a l y t i c a l aspects of bubble dynamics. J . Basic Eng. Trans. ASME. Vo l . 87 No. 4 I s a i a , J . ; G i r a r d , J . P. and Payan, P . : 1978. K i n e t i c study of g i l l epithel ium permeabi l i ty to water d i f f u s i o n in the f resh water t rou t , Salmo Ga i rdner i ; E f f e c t of adrenal ine . J . Membrane B i l o l . , 41 Jensen, J . : 1980. E f f e c t of TGP and t o t a l water hardness in Steelhead eggs and a l e v i n s . A progress repor t . Proc. N. W. F ish C u l t u r i s t s Conf. Courtney. B. C. Canada Jensen, J . ! 1984. Research B i o l o g i s t , P a c i f i c B i o l o g i c a l S t a t i o n , Nanaimo, B. C. (Personal Communication) Jones, D. R. and Randal l , D. J . : 1978. in F i sh Physiology Volume VII edited by Hoar and Randa l l , Academic Press . Liebermann, L . ; 1957. A i r Bubbles in Water. J . Appl . Phys ics , 28 Kiceniuk, J.W. and Jones, D . J . : 1977. The oxygen transport system in t rout during sustained exerc ise . J . Exp. B i o l . , 69 McElroy, W.D.; Whiteley, A . H . ; Warren, g .H. and Harvey, E . N . : 1944. Bubble formation in animals , Journal of C e l l u l a r and Comparative Physio logy, Volume 24, 1944 85 McLean, M.E. and Boreham, A . L .5 1980. The design and assessment of aerat ion towers. F i s h e r i e s and Oceans Canada Report. McLean, W. E . ; 1984. Personal communication reguarding supersaturat ion m o r t a l i t i e s at the Puntledge Hatchery during 1984. Meekin, T. A. and Turner, B. K.: 1974. Tolerance of Salmonid eggs, juven i les andsquafish to supersaturated n i t rogen. Wash. Dept. of F i s h e r i e s Tech Rept. 12:78-126 Matt, J . C . : 1957. In: The Physiology of F i shes ; Ed. M. E. Brown. Academic Press , New York Osipow, L. I.; 1972. Surface Chemisty - Theory and I i n d u s t r i a l App l i ca t ions ; Robert Kr ieger C o . ; Huntington, N.Y. Pease, D. C. and B l i n k s , L. R.: 1947. Cav i ta t ion from s o l i d surfaces in the absence of gas n u c l e i . J . of Phys ical and C o l l o i d a l Chem. Vo l . 51 Perry , R. H. and C h i l t o n , C. H . ; 1973. Chemical Engineers Handbook, F i f t h E d i t i o n ; McGraw H i l l . New York P h i l p , B . ; Inwood, M . J . ; and Warren, B .A . : 1972. Interact ions between gas bubbles and components of the blood: Impl icat ions in decompression s ickness . Aerospace Medicine, Sept. 1972 P l e s s e t , M. S. and Zwick, S. A . : 1954. The growth of vapor bubbles in superheated l i q u i d s . J . Appl . Phys ics . Vo l . 25, No. 4 P l e s s e t , M. S . : 1964. In :Cav i tat ion in rea l f l u i d s . Ed. by R. Dav is , American E l sev ie r Co. New York 86 P l e s s e t , M. S . : 1969. The t e n s i l e strength of l i q u i d s . Cav i tat ion State of Knowledge, ASME. Randa l l , D. J . and Jones, D. R.; 1972. The e f f e c t of deaf ferentat ion of the pseudobranch on the resp i ra to ry responce to hypoxia and hyperoxia in the t rout . Respiratory Physiology, (1973) 17 R a t c l i f f , G. A. and Ho ldcro f t , J . G . : 1963. D i f f u s i v i t i e s of gases in aqueous e l e c t r o l y t e s o l u t i o n s . Trans. Instn. Chem. Engrs. Vo l . 41 Re id , R. C , ; P rausn i t z , J . M. and Sherwood, T. K.s 1977. The proper t ies of Gasesand L i q u i d s . 3rd . ed. McGraw H i l l Co. New York. Schnute, J . and McKinnel l ; 1984. A b i o l o g i c a l meaningful approach to response surface a n a l y s i s . Can. J . F i s h . Aquat. S c i . 41:6 Shepherd, B.S. and MacDonald, D.D. 1980. The Aerat ion Workshop. Department of F i s h e r i e s and Oceans, Salmonid Enhancement Program. Sh i rahata , S . : 1966. Experiments on nitrogen gas disease with Rainbow trout f r y . B u l l e t i n of the Freshwater Research Laboratory. Tokyo 15:197-211 Stevens, E. D. and Randal l , D. J . : 1967. Changes of gas concentrat ions in blood and water during moderate swimming a c t i v i t y in Rainbow t rout . J . Expt. B i o l . 46 87 Stroud, R.K. : Bouck, G.R. and Nebeker, A.V. :1975. Pathology of acute and chronic exposure of salmonid f i s h e s to supersaturated water. In Chemistry and Physics of Aqueous So lut ions . W.A. Adams, Ed i to r . The Electrochemical Soc ie ty , P r inceton , New Jersey Vann, R.D. and C la rk , H .G. : 1975. Bubble growth and mechanical proper t ies of t i s s u e in decompression. Undersea Biomed. Res. 2. Weiss, R. F . : 1970. The s o l u b i l i t y of n i t rogen , oxygen and argon in water and sea water . , Deep Sea Research, Vo l . 17 Weitkamp, D.E. and Katz , Ii. 1980. A review of d isso lved gas supersaturat ion l i t e r a t u r e . Trans. Am. F i s h . Soc. 109:659-702 Welty, J . R . ; Wicks, C E . and Wilson, R . E . : 1976. Fundamentals of Momentum, Heat and Mass T r a n s f e r . , 2nd. Ed. John Wiley and Sons, New York Yang, W. J . and L iang , C. Y . ; 1972. Dynamics of d i s s o l u t i o n of gas bubbles or pockets in t i s s u e s . J . Biochem., 5 Yount, D. E . : 1979. App l i ca t ion of a bubble formation model to decompression s ickness in r a t s and humans. A v i a t i o n , Space and Environmental Medicine, Jan. Yount, D. E. and Yeung, C. M.: 1979. Determination of r a d i i of gas c a v i t a t i o n nucle i by f i l t e r i n g g e l a t i n . J . Acoust. Soc. Am. V o l . 65, No. 6 Yount, D. E. and L a l l y , D. A . : 1980. On the use of Oxygen to F a c i l i t a t e Decompression. A v i a t i o n , Space and Environmental Medicine, June 88 / Yount, D. E . : 1981. App l icat ion of a bubble formation model to decompression s ickness in f i n g e r l i n g salmon. Undersea Biomedical Research. Vo l . 8 , No.4 Yount, D. E . : 1983. A model fo r Microbuble f i s s i o n in sur factant s o l u t i o n s . J . of C o l l o i d a l and Interface Science. Vo l . 91, No. 2 Zwick, S. A . : 1954. The growth and co l lapse of vapor bubbles. Report No. 21 -19, Hydro. Lab. C a l i f . Inst. Tech. Zwick, S. A. and P l e s s e t , Ii. S . : 1955. On the dynamics of small vapor bubbles in l i q u i d s . J . Math. Phys ics . V o l . 33 89 1000 *1 c re z o *• r d •a •a M o» 0 re re (0 z o M • XI VO c o a* r+ H -O 3 hh O c 0* r+ re •1 DELTA P 1 0 0 . MM B HG. t 0 0 0 . HARUEY NUCLEATION MODEL SUPERSATURATED BUBBLE RELEASE SURFACE TENSION VS. TEMPERATURE FOR WATER AND HUMAN BLOOD 50 H 40 H i i i i i i I i 1 0 10 20 30 40 TEMPERATURE - DEG. C. WATER 0—\- HUMAN BLOOD g u r e N o . 4: P e n d a n t D r o p o f B l o o d w i t h D i m e n s i o n P a r a m e t e r s WATER TGP THRESHOLDS VS TEMPERATURE, Alt. = SEA LEVEL 1.3-, 0 4 8 12 16 20 24 28 TEMPERATURE - DEG. C. Figure No .6: Water TGP Thresholds Versus - Temperature •, J ' A l t . - S e a Level 95 1.22 WATER TGP THRESHOLDS VS TEMPERATURE, Alt = 700 M. 1.2-1 g 1.18H Ld 1 1.16 H w 2 1.14 H d 1 J 2 H fc 1 . H I Q 1.08 0 w 1.06 H Li I 1.04 H g 1.02 H h H 0.98 Ro=5uM Ro=10uM 0 i i — i — i — i — i — i — i — i — r 8 12 16 20 24 28 TEMPERATURE - DEG. C. F i g u r e No. 7: Water TGP Thresholds Versus Temperature, A l t . = 700 M 96 1.34 WATER TGP THRESHOLDS VS TEMPERATURE, Alt = 700 M. 1.32 4 1.3 H y (L If 1.28 H g 1.26-1 < 0 J 1.2 H I 0 1.18 - I j g 1.16-1 (/) * 1.12-1 1.06 Ro=5uM Ro=10uM Ro=20uM i i i i i — i — i — i — i — i — i — i — i — r 4 8 12 16 20 24 28 TEMPERATURE - DEG. C. F i g u r e No. 8: Water TGP Thresholds (Loc. Atm.) Versus Temperature, A l t i t u d e = 700 Meters 97 COMPENSATION DEPTH VS. TGP Alt = SEA LEVEL, TEMP. = 7 DEG. C. 5 n • SURFACE TENSION VS. TEMPERATURE 80.00 70.00 -\ 60.00 H O \ V) UJ z I z g w 50.00 LU o U) 40.00 -4 30.00 •WATER FISH BLOOD TEMPERATURE - DEG. C. HUMAN BLOOD X WATER/EXP. VARIATION OF TRANSPORT RATIOS AS A FUNCTION OF TEMPERATURE M 0 0 # M 0 I \ M Z 0 f N Z I i—i—i—i—r 20 24 28 TEMPERATURE - DEG. C. Figure No. 11: Va r ia t ion of Transport Ratios with Temperature 100 W hi n hi I Q. W 0 2 « 0 h o J 0 I ID hi H I h Q. 0 h TGP THRESHOLD FOR ARTERIAL BLOOD AS A FUNCTION OF WATER X'o 0 0.2 0.4 WATER X'o - F = 0.33 — Alt. = Sea Leval Depth = 0 M. F i g u r e v N o ^ ' ^ (F = 0.33) 101 TGP THRESHOLD POR ARTERIAL BLOOD AS A FUNCTION OF WATER Xo Ro=20uM 0 0.2 0.4 Xo — F = .67 — Alt.=Sea Level — Depth = 0 M. F i g u r e No. 13: TGP Thresholds f o r A r t e r i a l Blood Versus X'o, (F = 0.67) 102 TGP THRESHOLD FOR ARTERIAL BLOOD AS A FUNCTION OF WATER Xo (/) u K Ld I 0. if) 0 * Q h (/) Q J 0 I W Id C I h Q. 0 h Xo — F = .85 — AIt.=Sea Level — Depth = 0 M. ••Flxrare;*ito'v^l4i:^ (F =0.85) • 103 (fl hi hi I Q. (fl 0 Q h (fl Q J 0 I (fl hi i h Q. 0 h 1.4 1.35 1.3 1.25 1.2 4 1.15 H 1.H 1.05 H 1 H TGP THRESHOLD FOR ARTERIAL BLOOD AS A FUNCTION OF WATER X'o 0.95 -" Ro=5uM Ro=10uM Ro=20uM i 1 — i — 1 — F=.67 — 0.2 WATER X'o Alt.=700 M. 0.4 — DEPTH=0 M. F i g u r e No. 15: TGP Thresholds f o r A r t e r i a l Blood Versus X'o, ( A l t . = 700 M) 104 to hi a: hi i Q. W 0 2 h< * 0 h 0) 0 J 0 I 0) LU LY I h Q. 0 h TGP THRESHOLDS FOR ARTERIAL BLOOD AS A FUNCTION OF OXYGEN UPTAKE RATIO *o=0.21 Figure No OXYGEN UPTAKE RATIO - F — Alt. = Sea Leval — 16: TGP Thresholds for A r t e r i a l Blood Versus Os* Uptake Ratio 105 Temp. = 7 Deg. C. COMPENSATION DEPTH VS. TGP FOR ARTERIAL BLOOD 7-, . 1 1.2 1.4 1.6 1.8 2 TGP - STD. ATMOSPHERES — Alt=Sea Level — F=0.33 — Temp.=7 Deg. C. F i g u r e N o . 1 7 : C o m p e n s a t i o n D e p t h f o r A r t e r i a l B l o o d ( F = 0 . 3 3 ) 1 0 6 COMPENSATION DEPTH VS. TGP FOR ARTERIAL BLOOD 5 n 4 -2 Figure No. 18: Compensation Depth for A r t e r i a l Blood (F = 0.67) 107 COMPENSATION DEPTH VS. TGP FOR ARTERIAL BLOOD 5-1 • Figure No. 19: Compensation Depth for A r t e r i a l Blood (F = 0.85) 108 TGP THRESHOLDS FOR ARTERIAL BLOOD BLOOD PRESSURE = 40 mmHg, Ro=10uM, S.L w hi Lt Ld i Q. W 0 2 Q h 0 J 0 I hi Lt I h 0. 0 h WATER X'o A F=0.85 x F=0.67 v F=0.33 F i g u r e No. 20: TGP Thresholds f o r A r t e r i a l Blood with Pa = 40 mmHg. 109 TGP THRESHOLDS FOR VENOUS BLOOD AS A FUNCTION OF WATER X'o WATER X'o e N o . 21: T o t a l G a s P r e s s u r e T h r e s h o l d s f o r V e n o u s B l o o d V e r s u s X ' o 110 APPENDIX A EQUATION DERIVATION In t h i s appendix the developmental steps which led from Equations 3.8, 3.9, 3.14 and 3.15 to Equations 3.16 and 3.17 w i l l be presented. Equations 3.8, 3.9, 3.14 and 3.15 are respectively: dne/dt = (4IT/3RT) {3r2[P e(l - u ) - PM=»O] (dr/dt) + 46r(l - X A ) ( d r / d t ) - [P Er3 + 2€r2](dx*/dt)} Eq. 5.8 Eq. A . l dn^/dt = (4IT/3RT)[(P Er3 + 26r2) (dx*/dt) +x A(3P er2 + 46r)(dr/dt)] Eq. 5.9 Eq. A. 2 dn A/dt = 4 HADAL.IT; r ( P A D - X A C P E + (26/r)]} Eq. 5. 14 Eq. A. 3 dn B/dt = 4 HBDBI_IT r {PBO + Puzo - [P E + (26/r)](1 - X A ) } Eq. 5.15 Eq. A. 4 Here the equations have been re-numbered as A . l through A.4. If the r i g h t side of Equation A.2 i s set equal to the r i g h t side of Equation A.3 the following equation i s obtained. I l l R T H A D A L . [ P A O - x A ( P E + ( 2 6 / r ) ) ] = x A [ P E r + ( 4 6 / 3 ) ] ( d r / d t ) + ( r / 3 ) [ P E + ( 2 6 / r ) ] ( d x ^ / d t ) E q . A . 5 L i k e w i s e , i f t h e r i g h t s i d e o f E q u a t i o n A . l i s s e t e q u a l t o t h e r i g h t s i d e o f E q u a t i o n A . 4 a n e q u a t i o n o f t h e f o l l o w i n g f o r m i s o b t a i n e d . R T H B D BL. { P B O + P H 2 0 — [ P E + ( 2 6 / r ) ] t l - X A ] } = { r [ P e ( l - X A ) - P H 2 Q ] + ( 4 6 / 3 ) ( l - X A ) } ( d r / d t ) -(r/3)[Per + ( 2 6 / r ) ] [ d X A / d t ] E q . A . 6 I t w i l l b e n o t i c e d t h a t i f E q u a t i o n s A . 5 a n d A . 6 a r e a d d e d t o g e t h e r , t h e t e r m s c o n t a i n i n g d x A / d t w i l l s u b t r a c t o u t a n d a n e q u a t i o n i n t e r m s o f d r / d t w i l l b e o b t a i n e d . P e r f o r m i n g t h i s a d d i t i o n a n d r e a r r a n g i n g s o m e o f t h e t e r m s y i e l d s : d r / d t = R T { H A D A I _ C P A O - X A ( P E +(26/r ) ) ] + H B D B L [ P B O + P H 2 0 - (Pe + ( 2 6 7 r ) ) ( 1 - X A ) ] } / [ ( P e - P H 2 o ) r + ( 4 6 / 3 ) ] E q . A . 7 T h i s t h e n i s E q u a t i o n 3 . 1 6 o f t h e t e x t . I n o r d e r t o s i m p l i f y t h e d e v e l o p m e n t o f E q u a t i o n 5 . 1 7 , t w o d e f i n i t i o n s w i l l b e i n t r o d u c e d . 1 1 2 T h e s e a r e : 1p = H B D B U I P B O + P H 2 O - ( P B + ( 2 6 s / r ) ) ( l - X j ] = H A D AL. t P AO — X A ( P E + ( 2 6 / r ) ) ] U s i n g t h e s e d e f i n i t i o n s . E q u a t i o n s A . 5 a n d A . 6 c a n b e w r i t t e n a s : RTjtf = X A [ P B r + ( 4 6 / 3 ) ] ( d r / d t ) + ( r / 3 ) [ P K + ( 2 6 / r ) K d x A / d t ) E q . A . 8 RT l f = { r t P E ( l - X A ) - PH2O1 + ( 4 6 7 3 X 1 - X A ) } ( d r / d t ) - ( r / 3 ) [ P E + ( 2 6 / r ) ] [ d x A / d t ] E q . A . 9 I f n o w E q u a t i o n A . 8 i s m u l t i p l i e d b y dt/0 a n d E q u a t i o n A . 9 i s m u l t i p l i e d b y d t / l j J t h e f o l l o w i n g a r e o b t a i n e d . R T d t = (XAtPer + ( 4 6 / 3 ) ] d r + ( r / 3 ) [ P E + ( 2 6 / r ) ] dx A )/0 E q . A . 1 0 R T d t = [ < r [ P E ( l - X A ) - P H 2 O ] + ( 4 6 / 3 ) ( l - x A ) ) d r - ( r / 3 ) [ P « r + ( 2 6 / r ) ]dXA]/l)I E q . A . 1 1 S e t t i n g t h e r i g h t s i d e s o f t h e s e e q u a t i o n s e q u a l t o e a c h o t h e r a n d c o l l e c t i n g l i k e t e r m s y i e l d s : 1 1 3 t - l p x A [ P H r + (46/3)] + ^ { r [ P e ( l — X A ) — P H 2 D ] + (46/3X1 - X A ) ) ] d r = { t f ( r / 3 ) [ P E + (26 / r ) ] + p ( r / 3 ) [ P e + ( 2 6 7 r ) ] } d x A Eq. A.11 T h i s i n t u r n can be w r i t t e n as: d x A / d r = {0 { [ P e ( l - X A ) - P H 2 o ] r + (46/3)(1 - x A ) - U x A ( P E r + (46/3))} / [(If + 0 ) ( r / 3 ) ( P e + ( 2 6 / r ) ) ] Eq. A.12 which i s Equation 3.17 114 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0096083/manifest

Comment

Related Items