Basic Res. Cardiol. 74, 663-674 (1979) 9 1979 Dr. Dietrich Steinkopff Verlag, Darmstadt ISSN 0300-8428
D e p a r t m e n t o f Medicine, State University o f Buffalo, Buffalo, N e w Y o r k (USA)
Inert gas m e a s u r e m e n t of heterogeneous m y o c a r d i a l perfusion Messung heterogener Myokarddurehblutung mit der Fremdgasmethode P. Schanzenb~cher
a n d F. J. Klocke
With 7 figures (Received April 19, 1979)
Summary Inert gas m e a s u r e m e n t s of flow per unit weight (F/W) incorporating even saturation of heterogeneously perfused areas and two-decade resolution of coronary venous desaturation curves have been c o m p a r e d to radioactive m i cr o sp h er e measurements of F/W in closed-chest dogs with m o d e s t heterogeneity of F/W. Coefficients of variation for microsphere m e a s u r e m e n t s in 96 left ventricular segments revealed global heterogeneity of F/W, of similar degree, in animals with and without an abdominal aortie-caval fistula (18 +-_ 7 vs. 15 __ 4 per cent, p > 0.3). Endocardialepicardial flow ratios were lower in the fistula animals (1.05 __ 0.08 vs. 0.77 _+ 0.11, p < 0.01), reflecting transmural as well as spatial heterogeneity of F/W. Inert gas m e a s u r e m e n t s of average F/W, derived from the K e t y - S c h m i d t equation using dissolved h y d r o g e n (H2) as tracer, agreed within __ 20% of average microsphere F/W in 18 of 20 comparisons in fistula and non-fistula animals. Semilogarithmically plotted H 2 desaturation data were curvilinear in both settings but arbitrarily derived "slow c o m p a r t m e n t " H 2 FfW's agreed with m i cr o sp h er e endocardial F/W's only in the fistula animals. We conclude: (1) Methodologically adequate inert gas m e a s u r e m e n t s give accurate values for average F/W in the presence of m o d e r a t e spatial and/or transmural heterogeneity of perfusion; (2) A l t h o u g h the presence of heterogeneous perfusion can be appreciated from the shape of inert gas desaturation curves, compartmental analysis of curves involves major oversimplification of flow distribution and cannot be interpreted in a specific transmural or spatial sense without i n d ep en d e n t evidence that such flow patterns are present. Q u a n t i t a t i v e s t u d i e s of m y o c a r d i a l b l o o d f l o w i n m a n c o n t i n u e freq u e n t l y t o i n v o l v e i n e r t g a s t e c h n i q u e s , u s u a l l y w i t h t h e a i m of obtair~ing a n a v e r a g e v a l u e f o r f l o w p e r u n i t w e i g h t (F/W) f o r t h e e n t i r e l e f t v e n t r i c l e o r s o m e s e g m e n t t h e r e o f . I n s o m e s i t u a t i o n s , a t t e m p t s a r e m a d e to d e r i v e a n e s t i m a t e of f l o w d i s t r i b u t i o n w i t h i n t h e a r e a u n d e r s t u d y , e.g., b y m u l t i e x p o n e n t i a l c o m p a r t m e n t a l a n a l y s i s . A v a r i e t y of p o t e n t i a l p r o b lems, both theoretical and methodological, are well-recognized when flow S u p p o r t e d by P r o g r a m m - P r o j e c t Grant HLB-15194 from the National Heart, Blood and L u n g Institute. Dr. Schanzenb~cher is a Research Fellow of the Deutsche Forschungsgemeinschaft (Scha 291/1). Pr esen t ed in part at the 51st Scientific Meeting of the American Heart Association in Dallas, Texas, USA. 832
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i n f u s i o n l i n e w a s c l o s e d a b r u p t l y , so t h a t t h e L A D c a t h e t e r w a s i s o l a t e d f r o m t h e i n f u s a t e a n d a r t e r i a l S 2 i n f l o w c e a s e d i m m e d i a t e l y . 15-20 2.0 m l c o r o n a r y v e n o u s b l o o d s a m p l e s w e r e c o l l e c t e d i n g l a s s s y r i n g e s d u r i n g t h e l a s t t w o m i n u t e s of e a c h i n f u s i o n a n d for 12-15 m i n u t e s t h e r e a f t e r ; t h e f r e q u e n c y of s a m p l i n g w a s m o r e r a p i d d u r i n g t h e i n i t i a l p h a s e of d e s a t u r a t i o n , a n d b l o o d c l e a r e d f r o m t h e c a t h e t e r p r i o r to s a m p l i n g w a s c o n t i n u o u s l y r e t u r n e d to t h e a n i m a l . All s a m p l e s w e r e a n a l y z e d for H 2 c o n c e n t r a t i o n b y g a s c h r o m a t o g r a p h y , u s i n g v a c u u m e x t r a c t i o n of d i s s o l v e d g a s e s a n d a s p e c i a l l y d e s i g n e d t h e r m a l c o n d u c t i v i t y u n i t , as d e s c r i b e d p r e v i o u s l y (8). H 2 c o n c e n t r a t i o n w a s q u a n t i t a t e d f r o m t h e h e i g h t of t h e c h r o m a t o g r a p h i c H2 p e a k a n d e x p r e s s e d as a r b i t r a r y u n i t s p e r 2.0 m ] b l o o d s a m p l e . A v e r a g e F/W was calculated using the usual Kety-Schmidt equation: F / W = 100~,.
A Cv t fay dt
(1)
0
Where A Cv = the difference in coronary venous H 2 concentration between the o n s e t a n d t e r m i n a t i o n of d e s a t u r a t i o n ; St C v d t = t h e a r e a u n d e r t h e l i n e a r l y p l o t t e d v e n o u s d e s a t u r a t i o n c u r v e ; a n d St = t h e t i s s u e - b l o o d p a r t i t i o n c o e f f i c i e n t , h e r e t a k e n as 1.0 ml/g. ( S i n c e a r t e r i a l H 2 c o n c e n t r a t i o n is n e g l i g i b l e t h r o u g h o u t d e s a t u r a t i o n , it d o e s n o t a p p e a r i n t h e d e n o m i n a t o r , w h i c h r e p r e s e n t s t h e m e a n v e n o u s H 2 d i f f e r e n c e d u r i n g d e s a t u r a t i o n . ) C o r o n a r y v e n o u s H2 c o n c e n t r a t i o n - t i m e c u r v e s w e r e also p l o t t e d s e m i l o g a r i t h m i c a l l y o v e r a t w o - d e c a d e r a n g e . A s will b e d i s c u s s e d s u b s e q u e n t l y , a w e i g h t e d l e a s t - s q u a r e s r e g r e s s i o n l i n e (9) w a s f i t t e d t o t h e l o g a r i t h m of H 2 c o n c e n t r a t i o n vs. t i m e d u r i n g t h e s e c o n d d e c a d e of d e s a t u r a t i o n . A v a l u e of F / W for t h i s " s l o w c o m p a r t m e n t " w a s d e r i v e d f r o m t h e u s u a l e q u a t i o n for m o n o e x p o n e n t i a l c a l c u l a t i o n of F/W: .
.
0
.
0.693 F / W = 100 X - tO,--~
.
.
(2)
w h e r e t0.5 is t h e t i m e r e q u i r e d for v e n o u s H2 c o n c e n t r a t i o n to b e h a l v e d . (Arterial H 2 c o n c e n t r a t i o n is a g a i n c o n s i d e r e d n e g l i g i b l e f r o m t h e o n s e t of d e s a t u r a t i o n ; u n l i k e e q u a t i o n (1), t i s s u e - b l o o d d i f f u s i o n e q u i l i b r i u m is a s s u m e d ) .
Radioactive microsphere measurements T w o m i n u t e s b e f o r e t h e c o m p l e t i o n of e a c h H 2 i n f u s i o n , r a d i o l a b e l l e d 9 m i c r o s p h e r e s (3-M C o m p a n y , M i n n e a p o l i s , M i n n e s o t a ) s u s p e n d e d i n 10% d e x t r a n w i t h a f e w d r o p s of T w e e n - 8 0 w e r e i n j e c t e d i n t o t h e left a t r i u m o v e r a 2 0 - s e c o n d p e r i o d , a n d t h e a t r i a l c a t h e t e r f l u s h e d w i t h 10 cc of s a l i n e o v e r a n a d d i t i o n a l 10-15 s e c o n d s . A p p r o x i m a t e l y 3 x 10 v s p h e r e s w e r e p r e s e n t i n e a c h i n j e c t i o n ; t r a c e r s v a r i e d a m o n g e x p e r i m e n t s b u t i n c l u d e d 125I, 141Ce, 51Cr, 85Sr, 95Nb a n d 46Sc. T h e injections were not accompanied by detectable changes in aortic pressure or heart rate. C o l l e c t i o n of t h r e e t i m e d 3 0 - s e c o n d s a m p l e s f r o m e a c h of t h e t w o r e f e r e n c e s a m p l e c a t h e t e r s w a s b e g u n a f e w s e c o n d s p r i o r to e a c h i n j e c t i o n of s p h e r e s ; f l o w t h r o u g h e a c h c a t h e t e r w a s a d j u s t e d to - 12 c c / m i n a n d b l o o d a l l o w e d to d r i p i n t o w e i g h t e d c o l l e c t i o n v i a l s t o w h i c h 1 cc of h e p a r i n h a d b e e n a d d e d . V o l u m e s of t h e three successive samples varied by less than i5%. T h e d o g w a s s a c r i f i c e d a t t h e c o m p l e t i o n of t h e e x p e r i m e n t a n d t h e h e a r t r e m o v e d a n d p l a c e d i n 10% f o r m a l i n for 4-6 days. A f t e r r e m o v i n g b o t h a t r i a a n d t h e free w a l l of t h e r i g h t v e n t r i c l e , t h e left v e n t r i c l e w a s c u t i n t o five s e c t i o n s p a r a l l e l t o t h e m i t r a l v a l v e ring. T h e a p i c a l s e c t i o n w a s d i s c a r d e d a n d t h e f o u r r e m a i n i n g sections cut into eight wedges each. Each wedge was further subdivided into three t r a n s m u r a l layers, g i v i n g a t o t a l of 96 s e g m e n t s for t h e e n t i r e left v e n t r i c l e . E a c h t i s s u e s a m p l e w a s w e i g h e d a n d p l a c e d i n v i a l s for g a m m a c o u n t i n g a l o n g w i t h t h e
Sehanzenb~cher and Klocke, Inert gas m e a s u r e m e n t
665
is d i s t r i b u t e d h e t e r o g e n e o u s l y i n e i t h e r a s p a t i a l o r t r a n s m u r a l s e n s e (1). S t u d i e s v a l i d a t i n g i n e r t g a s m e a s u r e m e n t s i n t h e p r e s e n c e of a b n o r m a l h e t e r o g e n e i t y of flow are limited, and h a v e u s u a l l y i n v o l v e d p r e p a r a t i o n s w i t h w i d e e x t r e m e s of r e g i o n a l p e r f u s i o n , e.g., f o l l o w i n g t o t a l o c c l u s i o n of a m a j o r c o r o n a r y a r t e r i a l b r a n c h (2). I n a d d i t i o n , a l m o s t all v a l i d a t i o n studies in e i t h e r n o r m a l or a b n o r m a l states h a v e a n t e d a t e d the availability of t h e r a d i o a c t i v e m i c r o s p h e r e t e c h n i q u e (3), w h i c h h a s b e c o m e t h e experimental standard for defining flow heterogeneity and which prov i d e s a n i n d e p e n d e n t b a s i s f o r e v a l u a t i n g i n e r t g a s e s t i m a t e s of f l o w d i s t r i b u t i o n . T h e p r e s e n t s t u d i e s w e r e t h e r e f o r e u n d e r t a k e n (1) t o e v a l u a t e t h e d e g r e e of a g r e e m e n t b e t w e e n s i m u l t a n e o u s i n e r t g a s a n d m i c r o s p h e r e m e a s u r e m e n t s of a v e r a g e F / W i n t h e p r e s e n c e of m o d e s t s p a t i a l a n d / o r t r a n s m u r a l h e t e r o g e n e i t y of f l o w ; a n d (2) t o t e s t t h e d e g r e e t o w h i c h t h i s h e t e r o g e n e i t y , as d e f i n e d b y t h e m i c r o s p h e r e t e c h n i q u e , c a n b e a p p r e c i ated in the inert gas data.
Methods Thirteen closed-chest dogs weighing 20-35 kg were anesthetized with sodium pentobarbital, ventilated through a cuffed endotracheal t u b e with a Harvard respirator, and prepared for simultaneous m e a s u r e m e n t of myocardial blood flow by inert gas and microsphere techniques. The closed-chest preparation was chosen to avoid surface gas transfer, which can seriously complicate inert gas measurements in open-chest preparations (2, 4). U n d e r fluoroscopic control, an 8F catheter was advanced from a carotid artery retrograde into the left atrium for microsphere injection. A 4F catheter was inserted t h r o u g h the other carotid artery and positioned in the proximal portion of the left anterior descending coronary artery (LAD) for infusion of dissolved inert gas. A 7F Shirey catheter was inserted into the coronary sinus from an external jugular vein and advanced into the great cardiac vein for sampling of coronary venous inert gas concentration. A thoracic aortic catheter was used to monitor pressure and to sample systemic arterial blood during inert gas infusion. Two additional aortic catheters were used for m i cr o sp h er e reference arterial samples, in the fashion r e c o m m e n d e d by H e y m a n n (3). Six animals were studied w i th o u t additional instrumentation. On the basis of previous studies (5, 6), moderate spatial heterogeneity of left ventricular F/W was expected, i.e., values of F/W in 0.5-1.0 g segments were e x p e c t e d to vary appreciably, in a random fashion throughout all ventricular regions and layers. In the remaining seven dogs, the a b d o m e n was opened and a fistula created b e t w e e n the abdominal aorta and inferior vena cava below the renal arteries, using a 32 Bardex tube fitted with an adjustable external screw clamp. Th e aortic-caval fistula re d u ced m e a n diastolic pressure to 44 ___ 14 (SD) m m Hg (vs. 121 __ 18 m m Hg in non-fistula animals); transmural as well as spatial heterogeneity of F/W, with a re d u ced endocardial-epicardial flow ratio, was therefore e x p e c t e d (7). All animals were given heparin systemically to facilitate processing of blood samples. Inert gas m e a s u r e m e n t s Dissolved hydrogren (H z) was chosen as inert gas tracer because of its high degree of intrapulmonary elimination and its suitability for quantitation in coronar7 venous blood by gas chromatography. After drawing coronary venous H 2 " b l an k " samples (8), isotonic saline saturated with dissolved H 2 was infused into the LAD at a rate of 6.0 m l / m i n for 15-20 minutes, using a gear-driven infusion pump. Aortic blood was sampled near completion of each infusion, and recirculating H~ could n ev er be detected. At the termination of each infusion, a stopcock in the
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a r t e r i a l r e f e r e n c e s a m p l e s , u s i n g a 512 c h a n n e l m u l t i p l e r e g i o n of i n t e r e s t s y s t e m (Model 25601, N u c l e a r C h i c a g o , D e s P l a l n e s , Illinois) a n d s t a n d a r d r e g i o n of i n t e r e s t a n a l y s i s (3). F / W for e a c h of t h e 96 t i s s u e s a m p l e s w a s c a l c u l a t e d f r o m t h e u s u a l formula: RBF F/W = 10O C M 9 C R (3) w h e r e Cm = c p m p e r g of m y o c a r d i u m , C R = c p m i n t h e t o t a l r e f e r e n c e s a m p l e , a n d R B F = r e f e r e n c e s a m p l e flow r a t e (cc/min). C o u n t r a t e s p e r u n i t f l o w for t h e p a i r e d r e f e r e n c e s a m p l e s a l w a y s a g r e e d w i t h i n 12% a n d w e r e a v e r a g e d for t h e f i n a l d e t e r m i n a t i o n of F/W. A v e r a g e F / W for t h e e n t i r e v e n t r i c l e , a n d for e a c h of t h e t h r e e t r a n s m u r a l layers, w e r e also c a l c u l a t e d . I n a d d i t i o n , i n o r d e r t o c h a r a c t e r i z e t h e d i s t r i b u t i o n of F / W i n v e n o u s o u t f l o w ( w h i c h is w e i g h t e d t o w a r d h i g h e r v a l u e s of F/W), t h e f r a c t i o n of total outflow originating from each segment was calculated by expressing absolute o u t f l o w for t h e s e g m e n t (F/W-W) as a f r a c t i o n of s u m m a t e d a b s o l u t e o u t f l o w for all segments. Results
Figure 1 illustrates linear and semilogarithmic plots of coronary venous H2 d e s a t u r a t i o n c u r v e s f r o m a r e p r e s e n t a t i v e a n i m a l w i t h a n a o r t i c - c a v a l f i s t u l a . F i g u r e 2 s h o w s 2 0 c o m p a r i s o n s o f a v e r a g e F / W m e a s u r e d b y H2 a n d microspheres i n t h e 13 a n i m a l s s t u d i e d . F l o w s r a n g e f r o m - 4 0 t o 160 c c / min/100g; microsphere v a l u e s a v e r a g e 95 -4-_ 35 c c / m i n / 1 0 0 g i n f i s t u l a a n i m a l s a n d 89 _ 35 c c / m i n / 1 0 0 ? g i n n o n - f i s t u l a a n i m a l s . W i t h t w o e x c e p I00,
I00"
99
AVERAGE F/W = A C v xlO0 x X r :'=
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Fig. 1. C o r o n a r y v e n o u s d e s a t u r a t i o n i n a n a n i m a l w i t h a n a o r t i c - c a v a l fistula. A v e r a g e F / W is c a l c u l a t e d f r o m t h e l i n e a r l y p l o t t e d H 2 d e s a t u r a t i o n c u r v e , s h o w n o n t h e left, u s i n g t h e Kety-Schrnldt e q u a t i o n . T h e s a m e d a t a a r e p l o t t e d s e m i l o g a r i t h m i c a U y o n t h e right. A w e i g h t e d l e a s t - s q u a r e fit h a s b e e n a p p l i e d to t h e l o g a r i t h m s of d a t a p o i n t s i n t h e s e c o n d d e c a d e of d e s a t u r a t i o n t o o b t a i n a n a r b i t r a r y " s l o w c o m p a r t m e n t " F/W, u s i n g a m o n o e x p o n e n t i a l f u n c t i o n . (F/W = f l o w p e r u n i t weight)
667
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tions (both from the same animal), H 2 and microsphere F/W's agree within _ 20%. F i g u r e 3 s h o w s t h a t s e m i l o g a r i t h m i c H 2 c o n c e n t r a t i o n - t i m e c u r v e s w e r e c o n s i s t e n t l y c u r v i l i n e a r in b o t h f i s t u l a a n d n o n - f i s t u l a a n i m a l s . T h e 96 i n d i v i d u a l m i c r o s p h e r e m e a s u r e m e n t s of F / W s h o w e d c o n s i d e r a b l e v a r i a t i o n in e v e r y v e n t r i c l e . C o e f f i c i e n t s of v a r i a t i o n ( S D of t h e 96 m e a s u r e m e n t s ( w e i g h t e d for s a m p l e s i z e ) / a v e r a g e F / W • 100% a v e r a g e d 15 _ 4 in n o n f i s t u l a d o g s a n d 18 +_ 7 in f i s t u l a a n i m a l s (p > 0.3). E n d o c a r d i a l - e p i c a r d i a l f l o w ratios d i f f e r e d in t h e t w o s e t t i n g s , a v e r a g i n g 1.05 ___ I00 A
STULA
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Fig. 3. Semilogarithmically plotted H 2 desaturation curves for the first six minutes of desaturation in animals with and without aortic-caval fistulae.
668
B a s i c R e s e a r c h in CardioJogy, Vo]. 74, No. 6 (1979)
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Fig. 4. D i s t r i b u t i o n of F / W o b t a i n e d f r o m m i c r o s p h e r e m e a s u r e m e n t s i n 96 left ventricular segments in a fistula animal. For simplification, F/W's have been g r o u p e d a r b i t r a r i l y i n i n c r e m e n t s of 10 c c / m i n / 1 0 0 g . T h e o r d i n a t e s h o w s t h e perc e n t a g e of t o t a l left v e n t r i c u l a r o u t f l o w o r i g i n a t i n g f r o m s e g m e n t s h a v i n g t h e F / W ' s s h o w n o n t h e a b s c i s s a . N o t e t h e p r e p o n d e r a n c e of l o w F / W ' s i n t h e s u b e n docardium.
0.08 in non-fistula d o g s and 0.7'7 _ 0.11 in fistula animals (p < 0.01). Figures 4 and 5 illustrate representative e x a m p l e s of detailed F/W distributions. In the fistula animal (fig. 4), endocardial F/W's cluster in the lower, and e p i c a r d i a l F / W ' s i n t h e h i g h e r r a n g e of f l o w s . I n t h e n o n - f i s t u l a a n i m a l (fig. NO FISTULA
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Fig. 5. D i s t r i b u t i o n of F / W o b t a i n e d f r o m m i c r o s p h e r e m e a s u r e m e n t s i n 96 left
ventricular segments in a non-fistula animal. F o r simplification, F/W's have been g r o u p e d a r b i t r a r i l y i n i n c r e m e n t s of 10 c c / m i n / 1 0 0 g. T h e o r d i n a t e s h o w s t h e p e r c e n t a g e of t o t a l left v e n t r i c u l a r o u t f l o w o r i g i n a t i n g f r o m s e g m e n t s h a v i n g t h e F / W ' s s h o w n o n t h e a b s c i s s a . N o t e t h e u n i f o r m d i s t r i b u t i o n of F / W t h r o u g h o u t all t h r e e t r a n s m u r a l layers.
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Fig. 6. Comparison of average F/W in the s u b e n d o c a r d i u m (derived from microsphere measurements in 32 left ventricular segments) and "slow c o m p a r t m e n t " F/W (derived from the corresponding H 2 desaturation curve).
5), F / W ' s a r e s i m i l a r i n all t h r e e t r a n s m u r a l l a y e r s . T h i s p a t t e r n of f i n d i n g s was consistent in all animals studied. F i g u r e 6 c o m p a r e s t h e a r b i t r a r y " s l o w c o m p a r t m e n t " H2 F / W ' s d e r i v e d f r o m t h e s e c o n d d e c a d e of H2 d e s a t u r a t i o n w i t h c o r r e s p o n d i n g m i c r o s p h e r e v a l u e s of F / W i n t h e i n n e r t h i r d of t h e v e n t r i c l e . N i n e of t h e e l e v e n m e a s u r e m e n t s i n f i s t u l a a n i m a l s a g r e e w i t h i n _ 15%, w h i l e t h e s a m e a g r e e m e n t o c c u r s i n o n l y o n e of n i n e m e a s u r e m e n t s i n n o n - f i s t u l a a n i malso F i g u r e 7 i l l u s t r a t e s t h e s i m i l a r i t y of t w o e x p e r i m e n t a l H2 d e s a t u r a t i o n c u r v e s w i t h t h e o r e t i c a l v e n o u s o u t f l o w c u r v e s g e n e r a t e d f r o m t h e 96 m i c r o s p h e r e v a l u e s of F / W . A m o n o e x p o n e n t i a l d e s a t u r a t i o n w a s c a l c u l a t e d f o r e a c h of t h e 96 s e g m e n t s a n d a c o m p o s i t e 9 6 - c o m p a r t m e n t c u r v e g e n e r a t e d b y w e i g h t i n g t h e i n d i v i d u a l s e g m e n t s f o r t h e i r c o n t r i b u t i o n to venous outflow and summing them. Both examples show close corresp o n d e n c e b e t w e e n t h e c u r v i l i n e a r i t y of t h e m e a s u r e d H2 c u r v e a n d t h e generated microsphere curve.
Discussion T h e s e s t u d i e s i n d i c a t e t h a t v a l u e s for a v e r a g e F / W d e r i v e d f r o m H2 a n d m i c r o s p h e r e m e a s u r e m e n t s a g r e e c l o s e l y in t h e p r e s e n c e of h e t e r o g e n e o u s p e r f u s i o n , a n d t h a t h e t e r o g e n e o u s p e r f u s i o n is r e f l e c t e d in t h e s h a p e of i n e r t g a s v e n o u s d e s a t u r a t i o n c u r v e s . I n c o n s i d e r i n g t h e f i n d i n g s , s e v e r a l f e a t u r e s of t h e e x p e r i m e n t a l p r e p a r a t i o n n e e d to b e k e p t i n m i n d . T h e c h o i c e of H2 a s i n e r t g a s t r a c e r w a s i n t e n d e d t o e n s u r e n e g l i g i b l e s y s t e m i c a r t e r i a l t r a c e r c o n c e n t r a t i o n s d u r i n g d e s a t u r a t i o n . H2 l e a v i n g t h e m y o c a r d i u m in c o r o n a r y v e n o u s b l o o d w a s d i l u t e d , p r e s u m a b l y b y > 90%, a s it m i x e d w i t h s y s t e m i c v e n o u s r e t u r n i n t h e r i g h t h e a r t . I n a d d i t i o n , b e c a u s e of H2's l o w s o l u b i l i t y i n b l o o d (0.015 c c / m l / 7 6 0 m m Hg), t h e H2 c o n c e n t r a t i o n of m i x e d v e n o u s b l o o d s h o u l d h a v e b e e n r e d u c e d b y a n a d d i t i o n a l 9 5 - 9 8 % a s t h e b l o o d w a s e x p o s e d t o a l v e o l a r a i r (8). T h e a b s e n c e
670
Baslc Research in Cardiology, Vol. 74, No. 6 (1979) 100.
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TiME (minutes) Fig. 7. C o m p a r i s o n of measured H 2 desaturation curves and theoretical desaturation curves generated from microsphere data, using the formula shown. Each of the 96 left ventricular segments was considered to be perfused h o m o g en eo u sl y and for each s eg m en t a m o n o e x p o n e n t i a l curve was calculated (FjWi = flow per unit weight of each segment measured by microspheres). A 96 c o m p a r t m e n t multiexponential curve was then generated weighted according to the contribution of each seg m en t to the total venous outflow (Fi/Z Fi = p e r c e n t a g e of each individual seg m en t of the total venous outflow). C~t/Cv = fraction of original tracer concentration in venous outflow at time t. Two comparisons are shown. In both cases average H 2 FfW and average microsphere F/W agreed closely (42 vs 41 and 138 vs 139 cc/min/ 100 g). The good agreement b e t w e e n generated and measured washout curve confirms that the shape of the H2 desaturation curve actually reflects flow distributions which are measurable by microspheres.
of m e a s u r a b l e H 2 i n s y s t e m i c a r t e r i a l b l o o d s a m p l e d d u r i n g g 2 i n f u s i o n p r o v i d e d d i r e c t v e r i f i c a t i o n t h a t a r t e r i a l H2 c o n c e n t r a t i o n w a s i n d e e d n e g l i g i b l e t h r o u g h o u t d e s a t u r a t i o n . T h e 15-20 m i n u t e d u r a t i o n of H2 i n f u s i o n w a s i n t e n d e d t o a c h i e v e e v e n s a t u r a t i o n of a r e a s h a v i n g w i d e l y d i f f e r e n t p e r f u s i o n rates. T h e gas c h r o m a t o g r a p h i c analysis of H 2 c o n c e n t r a t i o n a l l o w e d v e n o u s H2 l e v e l s t o b e r e s o l v e d t o w i t h i n 1 - 2 % of t h o s e p r e s e n t at t h e o n s e t of d e s a t u r a t i o n . A s d i s c u s s e d p r e v i o u s l y (1), b o t h t h e s e p r e c a u t i o n s a r e i n t e n d e d t o g u a r a n t e e t h a t a r e a s of l o w F / W a r e f u l l y r e p r e s e n t e d i n t h e m e a s u r e m e n t of a v e r a g e F/W, a n d t h a t t h e l a t t e r is therefore not overestimated. In applying the radioactive microsphere technique, the precautions r e c e n t l y s u m m a r i z e d b y H e y m a n n (3) w e r e f o l l o w e d . T h e a g r e e m e n t of count rates per unit flow from the two arterial reference samples indicated t h a t a p p r o p r i a t e m i x i n g of s p h e r e s a n d b l o o d w a s a c h i e v e d i n t h e p a r t i c u -
Schanzenb~cher and Klocke, Inert gas measurement
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lar p r e p a r a t i o n e m p l o y e d . T h e n u m b e r of s p h e r e s r e a c h i n g e a c h of the 96 left v e n t r i c u l a r s e g m e n t s e x c e e d e d 1,000 in 19 of t h e 20 m e a s u r e m e n t s p e r f o r m e d . T h e decision to u s e all 96 s e g m e n t s in t h e c a l c u l a t i o n of a v e r a g e F/W w a s m a d e following a n inability to d e m o n s t r a t e a n y s y s t e m a tic d i f f e r e n c e b e t w e e n F/W c a l c u l a t e d for all 96 s e g m e n t s a n d F/W calculated o n l y for s e g m e n t s in t h e a n t e r o l a t e r a l v e n t r i c u l a r wall (p > 0.3, p a i r e d t). This a g r e e m e n t also s u p p o r t e d t h e u s e of H2 d e s a t u r a t i o n d e r i v e d f r o m L A D infusion as a reflection of F/W in t h e entire ventricle. T h e selective L A D i n f u s i o n m i n i m i z e d t h e v o l u m e of fluid w h i c h h a d to b e a d m i n i s t e r e d d u r i n g t h e relatively long s a t u r a t i o n period. I n t h r e e cases, m i c r o s p h e r e m e a s u r e m e n t s of a v e r a g e F/W w e r e r e p e a t e d at t h e t e r m i n a t i o n of H 2 desaturation; e a c h a g r e e d w i t h i n 10% of t h e v a l u e o b t a i n e d i m m e d i ately p r i o r to desaturation. T h e close a g r e e m e n t b e t w e e n H2 a n d m i c r o s p h e r e v a l u e s for a v e r a g e F/W (fig. 2) f u r t h e r v a l i d a t e s t h e u s e of the i n e r t gas a p p r o a c h in t h e p r e s e n c e of spatial a n d / o r t r a n s m u r a l h e t e r o g e n e i t y of flow. A l t h o u g h b o t h t e c h n i q u e s h a v e b e e n c o m p a r e d to direct m e a s u r e m e n t s of c o r o n a r y v e n o u s outflow in r i g h t h e a r t b y p a s s p r e p a r a t i o n s (2, 10), t h e p r e v i o u s inert gas v a l i d a t i o n d u r i n g " a b n o r m a l " states i n v o l v e d an e x t r e m e d e g r e e of h e t e r o g e n e o u s perfusion, p r o d u c e d b y c o r o n a r y arterial o c c l u s i o n (2). T h e p r e s e n t studies w i t h m i c r o s p h e r e s allow e v a l u a t i o n of inert gas m e a s u r e m e n t s a g a i n s t a n a p p r o p r i a t e l y v a l i d a t e d s t a n d a r d in t h e c l o s e d - c h e s t setting, w h e r e p o t e n t i a l l y serious difficulties r e l a t e d to s u r f a c e gas e x c h a n g e (4) are avoided. T h e t w o p o i n t s in figure 2 l o c a t e d o u t s i d e the +_ 20% a g r e e m e n t lines w e r e o b t a i n e d in t h e s a m e animal; no specific r e a s o n for t h e l a c k of a g r e e m e n t w a s identified. P r e v i o u s m i c r o s p h e r e s t u d i e s (5, 11, 12) a n d inert gas studies e m p l o y ing p r o l o n g e d p e r i o d s of s a t u r a t i o n a n d d e s a t u r a t i o n (13) h a v e i n d i c a t e d t h a t m y o c a r d i a l p e r f u s i o n is h e t e r o g e n e o u s in n o r m a l as well as a b n o r m a l states. T h e c u r r e n t s t u d i e s p r o v i d e a d d i t i o n a l v e r i f i c a t i o n of this o b s e r v a tion. T h e variability of m i c r o s p h e r e F/W v a l u e s in t h e p r e s e n t a n i m a l s is similar to t h a t r e p o r t e d b y Falsetti (5), Sest~er (11) a n d B a s s i n g t h w a i g h t e (12). T h e first t w o of t h e s e studies s u g g e s t t h a t a s u b s t a n t i a l p o r t i o n of variability in local F/W is related to m o m e n t - t o - m o m e n t c h a n g e s at t h e A l t h o u g h it is still u n c e r t a i n h o w p r e c i s e l y s p h e r e m e a s u r e m e n t s reflect flow v a r i a t i o n in s m a l l s e g m e n t s of tissue (14), t h e a g r e e m e n t of e x p e r i m e n t a l H2 c u r v e s a n d t h e o r e t i c a l d e s a t u r a t i o n c u r v e s g e n e r a g e d f r o m s p h e r e d a t a (fig. 7) s u g g e s t s t h a t t h e n o n - l i n e a r i t y of t h e s e m i l o g a r i t h m i c H2 c u r v e s is d u e p r i m a r i l y to h e t e r o g e n e o u s p e r f u s i o n , r a t h e r t h a n to m i c r o c i r c u l a t o r y level (without a n y c h a n g e in total arterial inflow). Bass i n g t h w a l g h t e ' s studies c o n c l u d e t h a t t h e d i s t r i b u t i o n of F/W, as m e a s u r e d b y m i c r o s p h e r e s in 250 s e g m e n t s of c o n s c i o u s b a b o o n ventricles, is similar u n d e r a v a r i e t y of p h y s i o l o g i c a l conditions. I n t h e Falsetti studies, a n d t h e p r e s e n t studies in n o n - f i s t u a l a n i m a l s (fig. 5), the variability of F/W in endocardial, m i d - m y o c a r d i a l , a n d e p i c a r d i a l layers is similar to t h a t for the entire ventricle, i.e., the h e t e r o g e n e i t y of F/W is p r i m a r i l y spatial r a t h e r t h a n t r a n s m u r a l . T h e p r e s e n t studies in fistula a n i m a l s (fig. 6) v e r i f y t h a t h e t e r o g e n e i t y of F/W w i t h i n i n d i v i d u a l layers persists e v e n w h e n a v e r a g e F/W for t h e layer is altered in relation to a v e r a g e F/W for t h e entire ventricle.
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factors s u c h as diffusion l i m i t a t i o n to gas e x c h a n g e , diffusional s h u n t i n g , etc. (15). T h e a r b i t r a r i l y c a l c u l a t e d " s l o w c o m p a r t m e n t " m e a s u r e m e n t s in figure 6 d e m o n s t r a t e t h a t c o m p a r t m e n t a l a n a l y s i s of diffusible t r a c e r d e s a t u r a t i o n c u r v e s involves m a j o r s i m p l i f i c a t i o n of in vivo p e r f u s i o n patterns. I n t h e fistula animals, values of F/W c a l c u l a t e d for the m o n o e x p o n e n t i a l s l o w c o m p a r t m e n t a g r e e r e a s o n a b l y well w i t h a v e r a g e mic r o s p h e r e F/W for the 32 s e g m e n t s in e a c h e n d o c a r d i a l layer. At t h e s a m e time, t h e h e t e r o g e n e i t y of e n d o c a r d i a l F]W r e v e a l e d b y t h e s p h e r e d a t a c a n n o t b e a p p r e c i a t e d in t h e H2 m e a s u r e m e n t s . Without i n d e p e n d e n t k n o w l e d g e t h a t t h e l o w e r v a l u e s of F]W originate f r o m t h e e n d o c a r d i u m , it w o u l d b e h a z a r d o u s to i n t e r p r e t t h e H2 d a t a as reflecting " a v e r a g e " F/W in t h e e n d o c a r d i u m , e.g., e p i c a r d i a l F/W is f r e q u e n t l y l o w e r t h a n e n d o c a r d i a l F/W in c o n s c i o u s a n i m a l s w i t h slow h e a r t r a t e s (16). T h e l a c k of a g r e e m e n t of H 2 s l o w c o m p a r t m e n t F/W's a n d s u b e n d o c a r d i a l m i c r o s p h e r e F/W's in n o n - f i s t u l a a n i m a l s a d d i t i o n a l l y illustrates t h a t spatial h e t e r o g e n e i t y of F/W in all m y o c a r d i a l layers c a n n o t b e d i s t i n g u i s h e d f r o m t r a n s m u r a l h e t e r o g e n e i t y on the basis of a n inert gas c u r v e alone. A l t h o u g h a v a r i e t y of m o r e c o m p l e x c o m p a r t m e n t a l a n d n o n - c o m p a r t m e n t a l a p p r o a c h e s for d e r i v i n g f l o w d i s t r i b u t i o n f r o m d e s a t u r a t i o n d a t a h a v e b e e n s u g g e s t e d , t h e y s e e m u n l i k e l y to c i r c u m v e n t t h e difficulties just outlined. T h e p r e s e n t d a t a h a v e b e e n s u b j e c t e d to t h e analysis sugg e s t e d b y V a n L l e w (17); h o w e v e r , s t a n d a r d d e v i a t i o n s of F]W's d e r i v e d f r o m s e m i l o g a r i t h m i c a l l y p l o t t e d H2 c u r v e s a g r e e d p o o r l y w i t h t h o s e available f r o m m i c r o s p h e r e m e a s u r e m e n t s . We h a v e also e x p r e s s e d desat u r a t i o n d a t a as L a p l a c e t r a n s f o r m s of f l o w d i s t r i b u t i o n s a n d a t t e m p t e d to u s e n u m e r i c a l p r o c e d u r e s to i n v e r t t h e t r a n s f o r m s a n d r e c o n s t r u c t t h e distributions. This a p p r o a c h p r o v e s to b e ill-conditioned m a t h e m a t i c a l l y , since qualitative c h a n g e s in t h e s h a p e of a d i s t r i b u t i o n often p r o d u c e v e r y m i n o r c h a n g e s in the d e s a t u r a t i o n curve. Qualitatively i n c o r r e c t distributions are r e c o v e r e d f r o m t h e e x p e r i m e n t a l c u r v e w h e n t h e s e c h a n g e s lie w i t h i n the b o u n d s of e x p e r i m e n t a l error, as is f r e q u e n t l y the case. T h u s , w h i l e c u r v i l i n e a r inert gas d e s a t u r a t i o n c u r v e s c a n r e a s o n a b l y b e interp r e t e d as i n d i c a t i n g overall h e t e r o g e n e i t y of p e r f u s i o n , specific i n t e r p r e t a tion a b o u t t h e p a t t e r n of h e t e r o g e n e i t y r e m a i n h a z a r d o u s w i t h p r e s e n t l y available t e c h n i q u e s .
Zusammens Myokarddurchblutungsmessungen w u r d e n simultan mit der Frerndgasrnethode u n d der Mikrosph~rentechnik bei H u n d e n mit u n d o h n e aortokavalen Shunt durchgeffihrf. N a c h uniformer Aufs~tfigung des Myokards rnit H 2 als Fremdgas w u r d e n Ents~ttigungskurven 61ber zwei logarithrnische D e k a d e n verfolgt. Die Variationskoeffizienten der Mikrosph~renmessungen in 96 linksventrikul~ren Segrnenten demonstrierfen globale HeterogenifAt der Durchblutung sowohl in den Versuchst/eren rnitals auch ohne aortokavalen Shunt (18 _+ 7 bzw. 15 _ 4 Prozent, p > 0,3).Das Verh~Itnis der endokardialen zur epikardialen Durchblutung war allerdings niedriger in den Tieren rnitaortokavalem Shunt (0,77 __-0,11 gegen61ber 1,05 --+ 0,08, p < 0,01) u n d zeigt sowohl r~urnliche wie auch transrnurale Heterogenit~t der Durchblutung. Die nach der Kety-Schmidt-Gleichung berechnete Durchschnittsdurchblutung des linken Ventrikels stirnrnteinnerhalb _+ 2 0 % in 18 von 20 Vergleichen mit den Mikrosphiirenmessungen fiberein.Sernilogarithmisch aufgezeichnete H2-Ents~ttigungskurven waren unter beiden Versuchsbedingungen gekriimrnt. Ein
Schanzenb~cher and Klocke, Inert gas m e a s u r e m e n t
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yon d e m terminalen Teil der Ents~ttigungskurve abgeleiteter ,,slow c o m p a r t m e n t " D u r ch b l u t u n g s we r t stimmte aber nur in den Versuchen mit aortokavalem S h u n t mit der E n d o k a r d d u r c h b l u t u n g ~berein. Folgende SchluBfolgerungen w u r d e n gezogen: 1. Methodisch exakte D u r c h b l u t u n g s m e s s u n g e n m i t der F r e m d g a s m e thode ergeben genaue Werte fOr die durchschnittliche D u r c h b l u t u n g des gesamten linken Ventrikels, w e n n die D u r c h b l u t u n g heterogen ist sowohl im transmuralen wie auch r~umlichen Sinne. 2. Obwohl heterogene D u r c h b l u t u n g s m u s t e r in der Gestalt yon Ents~ittigungskurven zum A u s d r u c k k o m m e n , beinhalten Kompartmentanalysen eine m e h r als grobe Vereinfachung der aktuellen Durchblutungsverh~iltnisse. Ohne unabh~ingige Kenntnis der tats~chlichen D u r ch b l u t u n g sv er t ei l u n g k6nnen sic nicht in einem spezifischen transmuralen oder r ~ u m h c h e n Sinn interpretiert werden. References I. Klocke, F. J.: Coronary blood flow in man. Prog. Cardiovasc, Dis. 19, 117 (I 976). 2. Klocke, F. J., I. L. Bunnell, D. G. Greene, S. M. Wittenberg, J. P. Visco: Average coronary blood flow per unit weight of left ventricle in patients with and without coronary artery disease. Circulation 50, 547 (1974). 3. Heymann, M. A., B. D. Payne, J. I. E. Hoffman, A. M. Rudolph: Blood flow measurements with radionuchde-labeled particles. Prog. Cardiovasc. Dis. 20, 55 (1977). 4. Gregg, D. E., F. H. Longino, P. A. Green, L. J. Czerwonka: A comparison of coronary flow d e t e r m i n e d by the nitrous oxide m e t h o d and by a direct m e t h o d using the rotameter. Circulation 3, 89 (1951). 5. Falsetti, H. L., R. J. Carroll, M. L. Marcus: Temporal heterogeneity of myocardial blood flow in anesthetized dogs. Circulation 52, 848 (1975). 6. Sestier, F., A. L 'Abbate, R. Mildenberger, L. Christie, G. K1assen: Microspheres to m eas u r e spatial and temporal heterogeneity of myocardial perfusion. Circulation 49 (III), 204 (1974). 7. Buckberg, G. 1)., D. E. Fixler, J. P. Archie, J. I. E. Hoffman: E x p e r i m e n t a l subendocardial ischemia in dogs with normal coronary arteries. Circ. Res. 30, 67 (1972). 8. Wittenberg, S. M., F. J. Klocke, D. G. Greene, I. L. Bunne11, H. L. Falsetti, J. A. Zizzi: Measurements of cardiac output in m a n with a nonrecirculating indicator. J. Clin. Invest. 50, 1466 (1971). 9. Riggs, 19. S.: T h e mathematical approach to physiological problems. (Cambridge-Massachusetts 1963). 10. Buekberg, G.D., J. C. L u c k , D. B. Payne, J. Z E. Hoffman, J. P. Archie, D. E. Fixler: S o m e source of error in measuring regional blood flow with radioactive microspheres. J. Appl. Physiol. 31, 598 (1971). 11. Sestier, F., H. Mildenberger, G. Klassen: Cyclic changes in coronary blood flow: A co n s eq u en c e of autoregulation. Circulation 51 (II), 126 (1975). 12. Bassingthwaighte, J. B., R. B. King, J. R. S. Hales, L. B. Rowel1, O. A. Smith: Stability of myocardial blood flow in awake, resting and stressed baboons. Circulation 56 (III), 35 (1977). 13. Klocke, F. J., R. C. Koberstein, D. E. Pittmann, D. G. Greene, D. R. Rosing: Effects of heterogeneous myocardial perfusion on coronary v e n o u s H 2 desaturation curves and calculations of coronary flow. J. Clin. Invest. 47, 2711 (1968). 14. Utley, J., E. L. Carlson, J. I. E. Hoffman, H. M. MarO'nez, G. D. Buckberg: Total and regional myocardial blood flow m e a s u r e m e n t s with 25 ~, 15 ~t, 9 ~t, and filtered 1-10 ~t diameter microspheres and antipyrine in dogs and sheep. Circ. Res. 34:391 (1974).
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15. Bassingthwaighte, J. B.: Physiology and theory of tracer washout techniques for the estimation of myocardial blood fl0w: flow extimation from tracer washout. Prog. Cardiovasc. Dis. 20, 155 (1977). 16. BaH, R. M., R. J. Baehe, R. C. Frederick, J. C. Greens Regional myocardial blood flow during graded treadmill exercise in the dog. J. Clin. Invest. 55, 43 (1975). 17. Van Liew, H. D.: Graphic analysis of aggregates of linear and exponential processes. J. Theoret. Biol. 16, 43 (1967). Authors' address: Peter Sehanzenb~cher, M.D., Abteilung III, Medizinische Klinik, 7400 Tfibingen, W. G e r m a n y
D e p a r t m e n t o f Medicine, State University o f Buffalo, Buffalo, N e w Y o r k (USA)
Inert gas m e a s u r e m e n t of heterogeneous m y o c a r d i a l perfusion Messung heterogener Myokarddurehblutung mit der Fremdgasmethode P. Schanzenb~cher
a n d F. J. Klocke
With 7 figures (Received April 19, 1979)
Summary Inert gas m e a s u r e m e n t s of flow per unit weight (F/W) incorporating even saturation of heterogeneously perfused areas and two-decade resolution of coronary venous desaturation curves have been c o m p a r e d to radioactive m i cr o sp h er e measurements of F/W in closed-chest dogs with m o d e s t heterogeneity of F/W. Coefficients of variation for microsphere m e a s u r e m e n t s in 96 left ventricular segments revealed global heterogeneity of F/W, of similar degree, in animals with and without an abdominal aortie-caval fistula (18 +-_ 7 vs. 15 __ 4 per cent, p > 0.3). Endocardialepicardial flow ratios were lower in the fistula animals (1.05 __ 0.08 vs. 0.77 _+ 0.11, p < 0.01), reflecting transmural as well as spatial heterogeneity of F/W. Inert gas m e a s u r e m e n t s of average F/W, derived from the K e t y - S c h m i d t equation using dissolved h y d r o g e n (H2) as tracer, agreed within __ 20% of average microsphere F/W in 18 of 20 comparisons in fistula and non-fistula animals. Semilogarithmically plotted H 2 desaturation data were curvilinear in both settings but arbitrarily derived "slow c o m p a r t m e n t " H 2 FfW's agreed with m i cr o sp h er e endocardial F/W's only in the fistula animals. We conclude: (1) Methodologically adequate inert gas m e a s u r e m e n t s give accurate values for average F/W in the presence of m o d e r a t e spatial and/or transmural heterogeneity of perfusion; (2) A l t h o u g h the presence of heterogeneous perfusion can be appreciated from the shape of inert gas desaturation curves, compartmental analysis of curves involves major oversimplification of flow distribution and cannot be interpreted in a specific transmural or spatial sense without i n d ep en d e n t evidence that such flow patterns are present. Q u a n t i t a t i v e s t u d i e s of m y o c a r d i a l b l o o d f l o w i n m a n c o n t i n u e freq u e n t l y t o i n v o l v e i n e r t g a s t e c h n i q u e s , u s u a l l y w i t h t h e a i m of obtair~ing a n a v e r a g e v a l u e f o r f l o w p e r u n i t w e i g h t (F/W) f o r t h e e n t i r e l e f t v e n t r i c l e o r s o m e s e g m e n t t h e r e o f . I n s o m e s i t u a t i o n s , a t t e m p t s a r e m a d e to d e r i v e a n e s t i m a t e of f l o w d i s t r i b u t i o n w i t h i n t h e a r e a u n d e r s t u d y , e.g., b y m u l t i e x p o n e n t i a l c o m p a r t m e n t a l a n a l y s i s . A v a r i e t y of p o t e n t i a l p r o b lems, both theoretical and methodological, are well-recognized when flow S u p p o r t e d by P r o g r a m m - P r o j e c t Grant HLB-15194 from the National Heart, Blood and L u n g Institute. Dr. Schanzenb~cher is a Research Fellow of the Deutsche Forschungsgemeinschaft (Scha 291/1). Pr esen t ed in part at the 51st Scientific Meeting of the American Heart Association in Dallas, Texas, USA. 832
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i n f u s i o n l i n e w a s c l o s e d a b r u p t l y , so t h a t t h e L A D c a t h e t e r w a s i s o l a t e d f r o m t h e i n f u s a t e a n d a r t e r i a l S 2 i n f l o w c e a s e d i m m e d i a t e l y . 15-20 2.0 m l c o r o n a r y v e n o u s b l o o d s a m p l e s w e r e c o l l e c t e d i n g l a s s s y r i n g e s d u r i n g t h e l a s t t w o m i n u t e s of e a c h i n f u s i o n a n d for 12-15 m i n u t e s t h e r e a f t e r ; t h e f r e q u e n c y of s a m p l i n g w a s m o r e r a p i d d u r i n g t h e i n i t i a l p h a s e of d e s a t u r a t i o n , a n d b l o o d c l e a r e d f r o m t h e c a t h e t e r p r i o r to s a m p l i n g w a s c o n t i n u o u s l y r e t u r n e d to t h e a n i m a l . All s a m p l e s w e r e a n a l y z e d for H 2 c o n c e n t r a t i o n b y g a s c h r o m a t o g r a p h y , u s i n g v a c u u m e x t r a c t i o n of d i s s o l v e d g a s e s a n d a s p e c i a l l y d e s i g n e d t h e r m a l c o n d u c t i v i t y u n i t , as d e s c r i b e d p r e v i o u s l y (8). H 2 c o n c e n t r a t i o n w a s q u a n t i t a t e d f r o m t h e h e i g h t of t h e c h r o m a t o g r a p h i c H2 p e a k a n d e x p r e s s e d as a r b i t r a r y u n i t s p e r 2.0 m ] b l o o d s a m p l e . A v e r a g e F/W was calculated using the usual Kety-Schmidt equation: F / W = 100~,.
A Cv t fay dt
(1)
0
Where A Cv = the difference in coronary venous H 2 concentration between the o n s e t a n d t e r m i n a t i o n of d e s a t u r a t i o n ; St C v d t = t h e a r e a u n d e r t h e l i n e a r l y p l o t t e d v e n o u s d e s a t u r a t i o n c u r v e ; a n d St = t h e t i s s u e - b l o o d p a r t i t i o n c o e f f i c i e n t , h e r e t a k e n as 1.0 ml/g. ( S i n c e a r t e r i a l H 2 c o n c e n t r a t i o n is n e g l i g i b l e t h r o u g h o u t d e s a t u r a t i o n , it d o e s n o t a p p e a r i n t h e d e n o m i n a t o r , w h i c h r e p r e s e n t s t h e m e a n v e n o u s H 2 d i f f e r e n c e d u r i n g d e s a t u r a t i o n . ) C o r o n a r y v e n o u s H2 c o n c e n t r a t i o n - t i m e c u r v e s w e r e also p l o t t e d s e m i l o g a r i t h m i c a l l y o v e r a t w o - d e c a d e r a n g e . A s will b e d i s c u s s e d s u b s e q u e n t l y , a w e i g h t e d l e a s t - s q u a r e s r e g r e s s i o n l i n e (9) w a s f i t t e d t o t h e l o g a r i t h m of H 2 c o n c e n t r a t i o n vs. t i m e d u r i n g t h e s e c o n d d e c a d e of d e s a t u r a t i o n . A v a l u e of F / W for t h i s " s l o w c o m p a r t m e n t " w a s d e r i v e d f r o m t h e u s u a l e q u a t i o n for m o n o e x p o n e n t i a l c a l c u l a t i o n of F/W: .
.
0
.
0.693 F / W = 100 X - tO,--~
.
.
(2)
w h e r e t0.5 is t h e t i m e r e q u i r e d for v e n o u s H2 c o n c e n t r a t i o n to b e h a l v e d . (Arterial H 2 c o n c e n t r a t i o n is a g a i n c o n s i d e r e d n e g l i g i b l e f r o m t h e o n s e t of d e s a t u r a t i o n ; u n l i k e e q u a t i o n (1), t i s s u e - b l o o d d i f f u s i o n e q u i l i b r i u m is a s s u m e d ) .
Radioactive microsphere measurements T w o m i n u t e s b e f o r e t h e c o m p l e t i o n of e a c h H 2 i n f u s i o n , r a d i o l a b e l l e d 9 m i c r o s p h e r e s (3-M C o m p a n y , M i n n e a p o l i s , M i n n e s o t a ) s u s p e n d e d i n 10% d e x t r a n w i t h a f e w d r o p s of T w e e n - 8 0 w e r e i n j e c t e d i n t o t h e left a t r i u m o v e r a 2 0 - s e c o n d p e r i o d , a n d t h e a t r i a l c a t h e t e r f l u s h e d w i t h 10 cc of s a l i n e o v e r a n a d d i t i o n a l 10-15 s e c o n d s . A p p r o x i m a t e l y 3 x 10 v s p h e r e s w e r e p r e s e n t i n e a c h i n j e c t i o n ; t r a c e r s v a r i e d a m o n g e x p e r i m e n t s b u t i n c l u d e d 125I, 141Ce, 51Cr, 85Sr, 95Nb a n d 46Sc. T h e injections were not accompanied by detectable changes in aortic pressure or heart rate. C o l l e c t i o n of t h r e e t i m e d 3 0 - s e c o n d s a m p l e s f r o m e a c h of t h e t w o r e f e r e n c e s a m p l e c a t h e t e r s w a s b e g u n a f e w s e c o n d s p r i o r to e a c h i n j e c t i o n of s p h e r e s ; f l o w t h r o u g h e a c h c a t h e t e r w a s a d j u s t e d to - 12 c c / m i n a n d b l o o d a l l o w e d to d r i p i n t o w e i g h t e d c o l l e c t i o n v i a l s t o w h i c h 1 cc of h e p a r i n h a d b e e n a d d e d . V o l u m e s of t h e three successive samples varied by less than i5%. T h e d o g w a s s a c r i f i c e d a t t h e c o m p l e t i o n of t h e e x p e r i m e n t a n d t h e h e a r t r e m o v e d a n d p l a c e d i n 10% f o r m a l i n for 4-6 days. A f t e r r e m o v i n g b o t h a t r i a a n d t h e free w a l l of t h e r i g h t v e n t r i c l e , t h e left v e n t r i c l e w a s c u t i n t o five s e c t i o n s p a r a l l e l t o t h e m i t r a l v a l v e ring. T h e a p i c a l s e c t i o n w a s d i s c a r d e d a n d t h e f o u r r e m a i n i n g sections cut into eight wedges each. Each wedge was further subdivided into three t r a n s m u r a l layers, g i v i n g a t o t a l of 96 s e g m e n t s for t h e e n t i r e left v e n t r i c l e . E a c h t i s s u e s a m p l e w a s w e i g h e d a n d p l a c e d i n v i a l s for g a m m a c o u n t i n g a l o n g w i t h t h e
Sehanzenb~cher and Klocke, Inert gas m e a s u r e m e n t
665
is d i s t r i b u t e d h e t e r o g e n e o u s l y i n e i t h e r a s p a t i a l o r t r a n s m u r a l s e n s e (1). S t u d i e s v a l i d a t i n g i n e r t g a s m e a s u r e m e n t s i n t h e p r e s e n c e of a b n o r m a l h e t e r o g e n e i t y of flow are limited, and h a v e u s u a l l y i n v o l v e d p r e p a r a t i o n s w i t h w i d e e x t r e m e s of r e g i o n a l p e r f u s i o n , e.g., f o l l o w i n g t o t a l o c c l u s i o n of a m a j o r c o r o n a r y a r t e r i a l b r a n c h (2). I n a d d i t i o n , a l m o s t all v a l i d a t i o n studies in e i t h e r n o r m a l or a b n o r m a l states h a v e a n t e d a t e d the availability of t h e r a d i o a c t i v e m i c r o s p h e r e t e c h n i q u e (3), w h i c h h a s b e c o m e t h e experimental standard for defining flow heterogeneity and which prov i d e s a n i n d e p e n d e n t b a s i s f o r e v a l u a t i n g i n e r t g a s e s t i m a t e s of f l o w d i s t r i b u t i o n . T h e p r e s e n t s t u d i e s w e r e t h e r e f o r e u n d e r t a k e n (1) t o e v a l u a t e t h e d e g r e e of a g r e e m e n t b e t w e e n s i m u l t a n e o u s i n e r t g a s a n d m i c r o s p h e r e m e a s u r e m e n t s of a v e r a g e F / W i n t h e p r e s e n c e of m o d e s t s p a t i a l a n d / o r t r a n s m u r a l h e t e r o g e n e i t y of f l o w ; a n d (2) t o t e s t t h e d e g r e e t o w h i c h t h i s h e t e r o g e n e i t y , as d e f i n e d b y t h e m i c r o s p h e r e t e c h n i q u e , c a n b e a p p r e c i ated in the inert gas data.
Methods Thirteen closed-chest dogs weighing 20-35 kg were anesthetized with sodium pentobarbital, ventilated through a cuffed endotracheal t u b e with a Harvard respirator, and prepared for simultaneous m e a s u r e m e n t of myocardial blood flow by inert gas and microsphere techniques. The closed-chest preparation was chosen to avoid surface gas transfer, which can seriously complicate inert gas measurements in open-chest preparations (2, 4). U n d e r fluoroscopic control, an 8F catheter was advanced from a carotid artery retrograde into the left atrium for microsphere injection. A 4F catheter was inserted t h r o u g h the other carotid artery and positioned in the proximal portion of the left anterior descending coronary artery (LAD) for infusion of dissolved inert gas. A 7F Shirey catheter was inserted into the coronary sinus from an external jugular vein and advanced into the great cardiac vein for sampling of coronary venous inert gas concentration. A thoracic aortic catheter was used to monitor pressure and to sample systemic arterial blood during inert gas infusion. Two additional aortic catheters were used for m i cr o sp h er e reference arterial samples, in the fashion r e c o m m e n d e d by H e y m a n n (3). Six animals were studied w i th o u t additional instrumentation. On the basis of previous studies (5, 6), moderate spatial heterogeneity of left ventricular F/W was expected, i.e., values of F/W in 0.5-1.0 g segments were e x p e c t e d to vary appreciably, in a random fashion throughout all ventricular regions and layers. In the remaining seven dogs, the a b d o m e n was opened and a fistula created b e t w e e n the abdominal aorta and inferior vena cava below the renal arteries, using a 32 Bardex tube fitted with an adjustable external screw clamp. Th e aortic-caval fistula re d u ced m e a n diastolic pressure to 44 ___ 14 (SD) m m Hg (vs. 121 __ 18 m m Hg in non-fistula animals); transmural as well as spatial heterogeneity of F/W, with a re d u ced endocardial-epicardial flow ratio, was therefore e x p e c t e d (7). All animals were given heparin systemically to facilitate processing of blood samples. Inert gas m e a s u r e m e n t s Dissolved hydrogren (H z) was chosen as inert gas tracer because of its high degree of intrapulmonary elimination and its suitability for quantitation in coronar7 venous blood by gas chromatography. After drawing coronary venous H 2 " b l an k " samples (8), isotonic saline saturated with dissolved H 2 was infused into the LAD at a rate of 6.0 m l / m i n for 15-20 minutes, using a gear-driven infusion pump. Aortic blood was sampled near completion of each infusion, and recirculating H~ could n ev er be detected. At the termination of each infusion, a stopcock in the
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a r t e r i a l r e f e r e n c e s a m p l e s , u s i n g a 512 c h a n n e l m u l t i p l e r e g i o n of i n t e r e s t s y s t e m (Model 25601, N u c l e a r C h i c a g o , D e s P l a l n e s , Illinois) a n d s t a n d a r d r e g i o n of i n t e r e s t a n a l y s i s (3). F / W for e a c h of t h e 96 t i s s u e s a m p l e s w a s c a l c u l a t e d f r o m t h e u s u a l formula: RBF F/W = 10O C M 9 C R (3) w h e r e Cm = c p m p e r g of m y o c a r d i u m , C R = c p m i n t h e t o t a l r e f e r e n c e s a m p l e , a n d R B F = r e f e r e n c e s a m p l e flow r a t e (cc/min). C o u n t r a t e s p e r u n i t f l o w for t h e p a i r e d r e f e r e n c e s a m p l e s a l w a y s a g r e e d w i t h i n 12% a n d w e r e a v e r a g e d for t h e f i n a l d e t e r m i n a t i o n of F/W. A v e r a g e F / W for t h e e n t i r e v e n t r i c l e , a n d for e a c h of t h e t h r e e t r a n s m u r a l layers, w e r e also c a l c u l a t e d . I n a d d i t i o n , i n o r d e r t o c h a r a c t e r i z e t h e d i s t r i b u t i o n of F / W i n v e n o u s o u t f l o w ( w h i c h is w e i g h t e d t o w a r d h i g h e r v a l u e s of F/W), t h e f r a c t i o n of total outflow originating from each segment was calculated by expressing absolute o u t f l o w for t h e s e g m e n t (F/W-W) as a f r a c t i o n of s u m m a t e d a b s o l u t e o u t f l o w for all segments. Results
Figure 1 illustrates linear and semilogarithmic plots of coronary venous H2 d e s a t u r a t i o n c u r v e s f r o m a r e p r e s e n t a t i v e a n i m a l w i t h a n a o r t i c - c a v a l f i s t u l a . F i g u r e 2 s h o w s 2 0 c o m p a r i s o n s o f a v e r a g e F / W m e a s u r e d b y H2 a n d microspheres i n t h e 13 a n i m a l s s t u d i e d . F l o w s r a n g e f r o m - 4 0 t o 160 c c / min/100g; microsphere v a l u e s a v e r a g e 95 -4-_ 35 c c / m i n / 1 0 0 g i n f i s t u l a a n i m a l s a n d 89 _ 35 c c / m i n / 1 0 0 ? g i n n o n - f i s t u l a a n i m a l s . W i t h t w o e x c e p I00,
I00"
99
AVERAGE F/W = A C v xlO0 x X r :'=
~o
80"
:D
3o-
"SLOWCOMPARTMENT" F/W _ 0.693 x I00 x .X
~
- ~
-
o o_
60Z
10-
_o n.-
40-
Z IM 0 Z 0 o 20-
0
o
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Fig. 1. C o r o n a r y v e n o u s d e s a t u r a t i o n i n a n a n i m a l w i t h a n a o r t i c - c a v a l fistula. A v e r a g e F / W is c a l c u l a t e d f r o m t h e l i n e a r l y p l o t t e d H 2 d e s a t u r a t i o n c u r v e , s h o w n o n t h e left, u s i n g t h e Kety-Schrnldt e q u a t i o n . T h e s a m e d a t a a r e p l o t t e d s e m i l o g a r i t h m i c a U y o n t h e right. A w e i g h t e d l e a s t - s q u a r e fit h a s b e e n a p p l i e d to t h e l o g a r i t h m s of d a t a p o i n t s i n t h e s e c o n d d e c a d e of d e s a t u r a t i o n t o o b t a i n a n a r b i t r a r y " s l o w c o m p a r t m e n t " F/W, u s i n g a m o n o e x p o n e n t i a l f u n c t i o n . (F/W = f l o w p e r u n i t weight)
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tions (both from the same animal), H 2 and microsphere F/W's agree within _ 20%. F i g u r e 3 s h o w s t h a t s e m i l o g a r i t h m i c H 2 c o n c e n t r a t i o n - t i m e c u r v e s w e r e c o n s i s t e n t l y c u r v i l i n e a r in b o t h f i s t u l a a n d n o n - f i s t u l a a n i m a l s . T h e 96 i n d i v i d u a l m i c r o s p h e r e m e a s u r e m e n t s of F / W s h o w e d c o n s i d e r a b l e v a r i a t i o n in e v e r y v e n t r i c l e . C o e f f i c i e n t s of v a r i a t i o n ( S D of t h e 96 m e a s u r e m e n t s ( w e i g h t e d for s a m p l e s i z e ) / a v e r a g e F / W • 100% a v e r a g e d 15 _ 4 in n o n f i s t u l a d o g s a n d 18 +_ 7 in f i s t u l a a n i m a l s (p > 0.3). E n d o c a r d i a l - e p i c a r d i a l f l o w ratios d i f f e r e d in t h e t w o s e t t i n g s , a v e r a g i n g 1.05 ___ I00 A
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Fig. 3. Semilogarithmically plotted H 2 desaturation curves for the first six minutes of desaturation in animals with and without aortic-caval fistulae.
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Fig. 4. D i s t r i b u t i o n of F / W o b t a i n e d f r o m m i c r o s p h e r e m e a s u r e m e n t s i n 96 left ventricular segments in a fistula animal. For simplification, F/W's have been g r o u p e d a r b i t r a r i l y i n i n c r e m e n t s of 10 c c / m i n / 1 0 0 g . T h e o r d i n a t e s h o w s t h e perc e n t a g e of t o t a l left v e n t r i c u l a r o u t f l o w o r i g i n a t i n g f r o m s e g m e n t s h a v i n g t h e F / W ' s s h o w n o n t h e a b s c i s s a . N o t e t h e p r e p o n d e r a n c e of l o w F / W ' s i n t h e s u b e n docardium.
0.08 in non-fistula d o g s and 0.7'7 _ 0.11 in fistula animals (p < 0.01). Figures 4 and 5 illustrate representative e x a m p l e s of detailed F/W distributions. In the fistula animal (fig. 4), endocardial F/W's cluster in the lower, and e p i c a r d i a l F / W ' s i n t h e h i g h e r r a n g e of f l o w s . I n t h e n o n - f i s t u l a a n i m a l (fig. NO FISTULA
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Fig. 5. D i s t r i b u t i o n of F / W o b t a i n e d f r o m m i c r o s p h e r e m e a s u r e m e n t s i n 96 left
ventricular segments in a non-fistula animal. F o r simplification, F/W's have been g r o u p e d a r b i t r a r i l y i n i n c r e m e n t s of 10 c c / m i n / 1 0 0 g. T h e o r d i n a t e s h o w s t h e p e r c e n t a g e of t o t a l left v e n t r i c u l a r o u t f l o w o r i g i n a t i n g f r o m s e g m e n t s h a v i n g t h e F / W ' s s h o w n o n t h e a b s c i s s a . N o t e t h e u n i f o r m d i s t r i b u t i o n of F / W t h r o u g h o u t all t h r e e t r a n s m u r a l layers.
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Fig. 6. Comparison of average F/W in the s u b e n d o c a r d i u m (derived from microsphere measurements in 32 left ventricular segments) and "slow c o m p a r t m e n t " F/W (derived from the corresponding H 2 desaturation curve).
5), F / W ' s a r e s i m i l a r i n all t h r e e t r a n s m u r a l l a y e r s . T h i s p a t t e r n of f i n d i n g s was consistent in all animals studied. F i g u r e 6 c o m p a r e s t h e a r b i t r a r y " s l o w c o m p a r t m e n t " H2 F / W ' s d e r i v e d f r o m t h e s e c o n d d e c a d e of H2 d e s a t u r a t i o n w i t h c o r r e s p o n d i n g m i c r o s p h e r e v a l u e s of F / W i n t h e i n n e r t h i r d of t h e v e n t r i c l e . N i n e of t h e e l e v e n m e a s u r e m e n t s i n f i s t u l a a n i m a l s a g r e e w i t h i n _ 15%, w h i l e t h e s a m e a g r e e m e n t o c c u r s i n o n l y o n e of n i n e m e a s u r e m e n t s i n n o n - f i s t u l a a n i malso F i g u r e 7 i l l u s t r a t e s t h e s i m i l a r i t y of t w o e x p e r i m e n t a l H2 d e s a t u r a t i o n c u r v e s w i t h t h e o r e t i c a l v e n o u s o u t f l o w c u r v e s g e n e r a t e d f r o m t h e 96 m i c r o s p h e r e v a l u e s of F / W . A m o n o e x p o n e n t i a l d e s a t u r a t i o n w a s c a l c u l a t e d f o r e a c h of t h e 96 s e g m e n t s a n d a c o m p o s i t e 9 6 - c o m p a r t m e n t c u r v e g e n e r a t e d b y w e i g h t i n g t h e i n d i v i d u a l s e g m e n t s f o r t h e i r c o n t r i b u t i o n to venous outflow and summing them. Both examples show close corresp o n d e n c e b e t w e e n t h e c u r v i l i n e a r i t y of t h e m e a s u r e d H2 c u r v e a n d t h e generated microsphere curve.
Discussion T h e s e s t u d i e s i n d i c a t e t h a t v a l u e s for a v e r a g e F / W d e r i v e d f r o m H2 a n d m i c r o s p h e r e m e a s u r e m e n t s a g r e e c l o s e l y in t h e p r e s e n c e of h e t e r o g e n e o u s p e r f u s i o n , a n d t h a t h e t e r o g e n e o u s p e r f u s i o n is r e f l e c t e d in t h e s h a p e of i n e r t g a s v e n o u s d e s a t u r a t i o n c u r v e s . I n c o n s i d e r i n g t h e f i n d i n g s , s e v e r a l f e a t u r e s of t h e e x p e r i m e n t a l p r e p a r a t i o n n e e d to b e k e p t i n m i n d . T h e c h o i c e of H2 a s i n e r t g a s t r a c e r w a s i n t e n d e d t o e n s u r e n e g l i g i b l e s y s t e m i c a r t e r i a l t r a c e r c o n c e n t r a t i o n s d u r i n g d e s a t u r a t i o n . H2 l e a v i n g t h e m y o c a r d i u m in c o r o n a r y v e n o u s b l o o d w a s d i l u t e d , p r e s u m a b l y b y > 90%, a s it m i x e d w i t h s y s t e m i c v e n o u s r e t u r n i n t h e r i g h t h e a r t . I n a d d i t i o n , b e c a u s e of H2's l o w s o l u b i l i t y i n b l o o d (0.015 c c / m l / 7 6 0 m m Hg), t h e H2 c o n c e n t r a t i o n of m i x e d v e n o u s b l o o d s h o u l d h a v e b e e n r e d u c e d b y a n a d d i t i o n a l 9 5 - 9 8 % a s t h e b l o o d w a s e x p o s e d t o a l v e o l a r a i r (8). T h e a b s e n c e
670
Baslc Research in Cardiology, Vol. 74, No. 6 (1979) 100.
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TiME (minutes) Fig. 7. C o m p a r i s o n of measured H 2 desaturation curves and theoretical desaturation curves generated from microsphere data, using the formula shown. Each of the 96 left ventricular segments was considered to be perfused h o m o g en eo u sl y and for each s eg m en t a m o n o e x p o n e n t i a l curve was calculated (FjWi = flow per unit weight of each segment measured by microspheres). A 96 c o m p a r t m e n t multiexponential curve was then generated weighted according to the contribution of each seg m en t to the total venous outflow (Fi/Z Fi = p e r c e n t a g e of each individual seg m en t of the total venous outflow). C~t/Cv = fraction of original tracer concentration in venous outflow at time t. Two comparisons are shown. In both cases average H 2 FfW and average microsphere F/W agreed closely (42 vs 41 and 138 vs 139 cc/min/ 100 g). The good agreement b e t w e e n generated and measured washout curve confirms that the shape of the H2 desaturation curve actually reflects flow distributions which are measurable by microspheres.
of m e a s u r a b l e H 2 i n s y s t e m i c a r t e r i a l b l o o d s a m p l e d d u r i n g g 2 i n f u s i o n p r o v i d e d d i r e c t v e r i f i c a t i o n t h a t a r t e r i a l H2 c o n c e n t r a t i o n w a s i n d e e d n e g l i g i b l e t h r o u g h o u t d e s a t u r a t i o n . T h e 15-20 m i n u t e d u r a t i o n of H2 i n f u s i o n w a s i n t e n d e d t o a c h i e v e e v e n s a t u r a t i o n of a r e a s h a v i n g w i d e l y d i f f e r e n t p e r f u s i o n rates. T h e gas c h r o m a t o g r a p h i c analysis of H 2 c o n c e n t r a t i o n a l l o w e d v e n o u s H2 l e v e l s t o b e r e s o l v e d t o w i t h i n 1 - 2 % of t h o s e p r e s e n t at t h e o n s e t of d e s a t u r a t i o n . A s d i s c u s s e d p r e v i o u s l y (1), b o t h t h e s e p r e c a u t i o n s a r e i n t e n d e d t o g u a r a n t e e t h a t a r e a s of l o w F / W a r e f u l l y r e p r e s e n t e d i n t h e m e a s u r e m e n t of a v e r a g e F/W, a n d t h a t t h e l a t t e r is therefore not overestimated. In applying the radioactive microsphere technique, the precautions r e c e n t l y s u m m a r i z e d b y H e y m a n n (3) w e r e f o l l o w e d . T h e a g r e e m e n t of count rates per unit flow from the two arterial reference samples indicated t h a t a p p r o p r i a t e m i x i n g of s p h e r e s a n d b l o o d w a s a c h i e v e d i n t h e p a r t i c u -
Schanzenb~cher and Klocke, Inert gas measurement
671
lar p r e p a r a t i o n e m p l o y e d . T h e n u m b e r of s p h e r e s r e a c h i n g e a c h of the 96 left v e n t r i c u l a r s e g m e n t s e x c e e d e d 1,000 in 19 of t h e 20 m e a s u r e m e n t s p e r f o r m e d . T h e decision to u s e all 96 s e g m e n t s in t h e c a l c u l a t i o n of a v e r a g e F/W w a s m a d e following a n inability to d e m o n s t r a t e a n y s y s t e m a tic d i f f e r e n c e b e t w e e n F/W c a l c u l a t e d for all 96 s e g m e n t s a n d F/W calculated o n l y for s e g m e n t s in t h e a n t e r o l a t e r a l v e n t r i c u l a r wall (p > 0.3, p a i r e d t). This a g r e e m e n t also s u p p o r t e d t h e u s e of H2 d e s a t u r a t i o n d e r i v e d f r o m L A D infusion as a reflection of F/W in t h e entire ventricle. T h e selective L A D i n f u s i o n m i n i m i z e d t h e v o l u m e of fluid w h i c h h a d to b e a d m i n i s t e r e d d u r i n g t h e relatively long s a t u r a t i o n period. I n t h r e e cases, m i c r o s p h e r e m e a s u r e m e n t s of a v e r a g e F/W w e r e r e p e a t e d at t h e t e r m i n a t i o n of H 2 desaturation; e a c h a g r e e d w i t h i n 10% of t h e v a l u e o b t a i n e d i m m e d i ately p r i o r to desaturation. T h e close a g r e e m e n t b e t w e e n H2 a n d m i c r o s p h e r e v a l u e s for a v e r a g e F/W (fig. 2) f u r t h e r v a l i d a t e s t h e u s e of the i n e r t gas a p p r o a c h in t h e p r e s e n c e of spatial a n d / o r t r a n s m u r a l h e t e r o g e n e i t y of flow. A l t h o u g h b o t h t e c h n i q u e s h a v e b e e n c o m p a r e d to direct m e a s u r e m e n t s of c o r o n a r y v e n o u s outflow in r i g h t h e a r t b y p a s s p r e p a r a t i o n s (2, 10), t h e p r e v i o u s inert gas v a l i d a t i o n d u r i n g " a b n o r m a l " states i n v o l v e d an e x t r e m e d e g r e e of h e t e r o g e n e o u s perfusion, p r o d u c e d b y c o r o n a r y arterial o c c l u s i o n (2). T h e p r e s e n t studies w i t h m i c r o s p h e r e s allow e v a l u a t i o n of inert gas m e a s u r e m e n t s a g a i n s t a n a p p r o p r i a t e l y v a l i d a t e d s t a n d a r d in t h e c l o s e d - c h e s t setting, w h e r e p o t e n t i a l l y serious difficulties r e l a t e d to s u r f a c e gas e x c h a n g e (4) are avoided. T h e t w o p o i n t s in figure 2 l o c a t e d o u t s i d e the +_ 20% a g r e e m e n t lines w e r e o b t a i n e d in t h e s a m e animal; no specific r e a s o n for t h e l a c k of a g r e e m e n t w a s identified. P r e v i o u s m i c r o s p h e r e s t u d i e s (5, 11, 12) a n d inert gas studies e m p l o y ing p r o l o n g e d p e r i o d s of s a t u r a t i o n a n d d e s a t u r a t i o n (13) h a v e i n d i c a t e d t h a t m y o c a r d i a l p e r f u s i o n is h e t e r o g e n e o u s in n o r m a l as well as a b n o r m a l states. T h e c u r r e n t s t u d i e s p r o v i d e a d d i t i o n a l v e r i f i c a t i o n of this o b s e r v a tion. T h e variability of m i c r o s p h e r e F/W v a l u e s in t h e p r e s e n t a n i m a l s is similar to t h a t r e p o r t e d b y Falsetti (5), Sest~er (11) a n d B a s s i n g t h w a i g h t e (12). T h e first t w o of t h e s e studies s u g g e s t t h a t a s u b s t a n t i a l p o r t i o n of variability in local F/W is related to m o m e n t - t o - m o m e n t c h a n g e s at t h e A l t h o u g h it is still u n c e r t a i n h o w p r e c i s e l y s p h e r e m e a s u r e m e n t s reflect flow v a r i a t i o n in s m a l l s e g m e n t s of tissue (14), t h e a g r e e m e n t of e x p e r i m e n t a l H2 c u r v e s a n d t h e o r e t i c a l d e s a t u r a t i o n c u r v e s g e n e r a g e d f r o m s p h e r e d a t a (fig. 7) s u g g e s t s t h a t t h e n o n - l i n e a r i t y of t h e s e m i l o g a r i t h m i c H2 c u r v e s is d u e p r i m a r i l y to h e t e r o g e n e o u s p e r f u s i o n , r a t h e r t h a n to m i c r o c i r c u l a t o r y level (without a n y c h a n g e in total arterial inflow). Bass i n g t h w a l g h t e ' s studies c o n c l u d e t h a t t h e d i s t r i b u t i o n of F/W, as m e a s u r e d b y m i c r o s p h e r e s in 250 s e g m e n t s of c o n s c i o u s b a b o o n ventricles, is similar u n d e r a v a r i e t y of p h y s i o l o g i c a l conditions. I n t h e Falsetti studies, a n d t h e p r e s e n t studies in n o n - f i s t u a l a n i m a l s (fig. 5), the variability of F/W in endocardial, m i d - m y o c a r d i a l , a n d e p i c a r d i a l layers is similar to t h a t for the entire ventricle, i.e., the h e t e r o g e n e i t y of F/W is p r i m a r i l y spatial r a t h e r t h a n t r a n s m u r a l . T h e p r e s e n t studies in fistula a n i m a l s (fig. 6) v e r i f y t h a t h e t e r o g e n e i t y of F/W w i t h i n i n d i v i d u a l layers persists e v e n w h e n a v e r a g e F/W for t h e layer is altered in relation to a v e r a g e F/W for t h e entire ventricle.
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Baslc Research in Cardiology, Vol. 74, No. 6 (1979)
factors s u c h as diffusion l i m i t a t i o n to gas e x c h a n g e , diffusional s h u n t i n g , etc. (15). T h e a r b i t r a r i l y c a l c u l a t e d " s l o w c o m p a r t m e n t " m e a s u r e m e n t s in figure 6 d e m o n s t r a t e t h a t c o m p a r t m e n t a l a n a l y s i s of diffusible t r a c e r d e s a t u r a t i o n c u r v e s involves m a j o r s i m p l i f i c a t i o n of in vivo p e r f u s i o n patterns. I n t h e fistula animals, values of F/W c a l c u l a t e d for the m o n o e x p o n e n t i a l s l o w c o m p a r t m e n t a g r e e r e a s o n a b l y well w i t h a v e r a g e mic r o s p h e r e F/W for the 32 s e g m e n t s in e a c h e n d o c a r d i a l layer. At t h e s a m e time, t h e h e t e r o g e n e i t y of e n d o c a r d i a l F]W r e v e a l e d b y t h e s p h e r e d a t a c a n n o t b e a p p r e c i a t e d in t h e H2 m e a s u r e m e n t s . Without i n d e p e n d e n t k n o w l e d g e t h a t t h e l o w e r v a l u e s of F]W originate f r o m t h e e n d o c a r d i u m , it w o u l d b e h a z a r d o u s to i n t e r p r e t t h e H2 d a t a as reflecting " a v e r a g e " F/W in t h e e n d o c a r d i u m , e.g., e p i c a r d i a l F/W is f r e q u e n t l y l o w e r t h a n e n d o c a r d i a l F/W in c o n s c i o u s a n i m a l s w i t h slow h e a r t r a t e s (16). T h e l a c k of a g r e e m e n t of H 2 s l o w c o m p a r t m e n t F/W's a n d s u b e n d o c a r d i a l m i c r o s p h e r e F/W's in n o n - f i s t u l a a n i m a l s a d d i t i o n a l l y illustrates t h a t spatial h e t e r o g e n e i t y of F/W in all m y o c a r d i a l layers c a n n o t b e d i s t i n g u i s h e d f r o m t r a n s m u r a l h e t e r o g e n e i t y on the basis of a n inert gas c u r v e alone. A l t h o u g h a v a r i e t y of m o r e c o m p l e x c o m p a r t m e n t a l a n d n o n - c o m p a r t m e n t a l a p p r o a c h e s for d e r i v i n g f l o w d i s t r i b u t i o n f r o m d e s a t u r a t i o n d a t a h a v e b e e n s u g g e s t e d , t h e y s e e m u n l i k e l y to c i r c u m v e n t t h e difficulties just outlined. T h e p r e s e n t d a t a h a v e b e e n s u b j e c t e d to t h e analysis sugg e s t e d b y V a n L l e w (17); h o w e v e r , s t a n d a r d d e v i a t i o n s of F]W's d e r i v e d f r o m s e m i l o g a r i t h m i c a l l y p l o t t e d H2 c u r v e s a g r e e d p o o r l y w i t h t h o s e available f r o m m i c r o s p h e r e m e a s u r e m e n t s . We h a v e also e x p r e s s e d desat u r a t i o n d a t a as L a p l a c e t r a n s f o r m s of f l o w d i s t r i b u t i o n s a n d a t t e m p t e d to u s e n u m e r i c a l p r o c e d u r e s to i n v e r t t h e t r a n s f o r m s a n d r e c o n s t r u c t t h e distributions. This a p p r o a c h p r o v e s to b e ill-conditioned m a t h e m a t i c a l l y , since qualitative c h a n g e s in t h e s h a p e of a d i s t r i b u t i o n often p r o d u c e v e r y m i n o r c h a n g e s in the d e s a t u r a t i o n curve. Qualitatively i n c o r r e c t distributions are r e c o v e r e d f r o m t h e e x p e r i m e n t a l c u r v e w h e n t h e s e c h a n g e s lie w i t h i n the b o u n d s of e x p e r i m e n t a l error, as is f r e q u e n t l y the case. T h u s , w h i l e c u r v i l i n e a r inert gas d e s a t u r a t i o n c u r v e s c a n r e a s o n a b l y b e interp r e t e d as i n d i c a t i n g overall h e t e r o g e n e i t y of p e r f u s i o n , specific i n t e r p r e t a tion a b o u t t h e p a t t e r n of h e t e r o g e n e i t y r e m a i n h a z a r d o u s w i t h p r e s e n t l y available t e c h n i q u e s .
Zusammens Myokarddurchblutungsmessungen w u r d e n simultan mit der Frerndgasrnethode u n d der Mikrosph~rentechnik bei H u n d e n mit u n d o h n e aortokavalen Shunt durchgeffihrf. N a c h uniformer Aufs~tfigung des Myokards rnit H 2 als Fremdgas w u r d e n Ents~ttigungskurven 61ber zwei logarithrnische D e k a d e n verfolgt. Die Variationskoeffizienten der Mikrosph~renmessungen in 96 linksventrikul~ren Segrnenten demonstrierfen globale HeterogenifAt der Durchblutung sowohl in den Versuchst/eren rnitals auch ohne aortokavalen Shunt (18 _+ 7 bzw. 15 _ 4 Prozent, p > 0,3).Das Verh~Itnis der endokardialen zur epikardialen Durchblutung war allerdings niedriger in den Tieren rnitaortokavalem Shunt (0,77 __-0,11 gegen61ber 1,05 --+ 0,08, p < 0,01) u n d zeigt sowohl r~urnliche wie auch transrnurale Heterogenit~t der Durchblutung. Die nach der Kety-Schmidt-Gleichung berechnete Durchschnittsdurchblutung des linken Ventrikels stirnrnteinnerhalb _+ 2 0 % in 18 von 20 Vergleichen mit den Mikrosphiirenmessungen fiberein.Sernilogarithmisch aufgezeichnete H2-Ents~ttigungskurven waren unter beiden Versuchsbedingungen gekriimrnt. Ein
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yon d e m terminalen Teil der Ents~ttigungskurve abgeleiteter ,,slow c o m p a r t m e n t " D u r ch b l u t u n g s we r t stimmte aber nur in den Versuchen mit aortokavalem S h u n t mit der E n d o k a r d d u r c h b l u t u n g ~berein. Folgende SchluBfolgerungen w u r d e n gezogen: 1. Methodisch exakte D u r c h b l u t u n g s m e s s u n g e n m i t der F r e m d g a s m e thode ergeben genaue Werte fOr die durchschnittliche D u r c h b l u t u n g des gesamten linken Ventrikels, w e n n die D u r c h b l u t u n g heterogen ist sowohl im transmuralen wie auch r~umlichen Sinne. 2. Obwohl heterogene D u r c h b l u t u n g s m u s t e r in der Gestalt yon Ents~ittigungskurven zum A u s d r u c k k o m m e n , beinhalten Kompartmentanalysen eine m e h r als grobe Vereinfachung der aktuellen Durchblutungsverh~iltnisse. Ohne unabh~ingige Kenntnis der tats~chlichen D u r ch b l u t u n g sv er t ei l u n g k6nnen sic nicht in einem spezifischen transmuralen oder r ~ u m h c h e n Sinn interpretiert werden. References I. Klocke, F. J.: Coronary blood flow in man. Prog. Cardiovasc, Dis. 19, 117 (I 976). 2. Klocke, F. J., I. L. Bunnell, D. G. Greene, S. M. Wittenberg, J. P. Visco: Average coronary blood flow per unit weight of left ventricle in patients with and without coronary artery disease. Circulation 50, 547 (1974). 3. Heymann, M. A., B. D. Payne, J. I. E. Hoffman, A. M. Rudolph: Blood flow measurements with radionuchde-labeled particles. Prog. Cardiovasc. Dis. 20, 55 (1977). 4. Gregg, D. E., F. H. Longino, P. A. Green, L. J. Czerwonka: A comparison of coronary flow d e t e r m i n e d by the nitrous oxide m e t h o d and by a direct m e t h o d using the rotameter. Circulation 3, 89 (1951). 5. Falsetti, H. L., R. J. Carroll, M. L. Marcus: Temporal heterogeneity of myocardial blood flow in anesthetized dogs. Circulation 52, 848 (1975). 6. Sestier, F., A. L 'Abbate, R. Mildenberger, L. Christie, G. K1assen: Microspheres to m eas u r e spatial and temporal heterogeneity of myocardial perfusion. Circulation 49 (III), 204 (1974). 7. Buckberg, G. 1)., D. E. Fixler, J. P. Archie, J. I. E. Hoffman: E x p e r i m e n t a l subendocardial ischemia in dogs with normal coronary arteries. Circ. Res. 30, 67 (1972). 8. Wittenberg, S. M., F. J. Klocke, D. G. Greene, I. L. Bunne11, H. L. Falsetti, J. A. Zizzi: Measurements of cardiac output in m a n with a nonrecirculating indicator. J. Clin. Invest. 50, 1466 (1971). 9. Riggs, 19. S.: T h e mathematical approach to physiological problems. (Cambridge-Massachusetts 1963). 10. Buekberg, G.D., J. C. L u c k , D. B. Payne, J. Z E. Hoffman, J. P. Archie, D. E. Fixler: S o m e source of error in measuring regional blood flow with radioactive microspheres. J. Appl. Physiol. 31, 598 (1971). 11. Sestier, F., H. Mildenberger, G. Klassen: Cyclic changes in coronary blood flow: A co n s eq u en c e of autoregulation. Circulation 51 (II), 126 (1975). 12. Bassingthwaighte, J. B., R. B. King, J. R. S. Hales, L. B. Rowel1, O. A. Smith: Stability of myocardial blood flow in awake, resting and stressed baboons. Circulation 56 (III), 35 (1977). 13. Klocke, F. J., R. C. Koberstein, D. E. Pittmann, D. G. Greene, D. R. Rosing: Effects of heterogeneous myocardial perfusion on coronary v e n o u s H 2 desaturation curves and calculations of coronary flow. J. Clin. Invest. 47, 2711 (1968). 14. Utley, J., E. L. Carlson, J. I. E. Hoffman, H. M. MarO'nez, G. D. Buckberg: Total and regional myocardial blood flow m e a s u r e m e n t s with 25 ~, 15 ~t, 9 ~t, and filtered 1-10 ~t diameter microspheres and antipyrine in dogs and sheep. Circ. Res. 34:391 (1974).
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15. Bassingthwaighte, J. B.: Physiology and theory of tracer washout techniques for the estimation of myocardial blood fl0w: flow extimation from tracer washout. Prog. Cardiovasc. Dis. 20, 155 (1977). 16. BaH, R. M., R. J. Baehe, R. C. Frederick, J. C. Greens Regional myocardial blood flow during graded treadmill exercise in the dog. J. Clin. Invest. 55, 43 (1975). 17. Van Liew, H. D.: Graphic analysis of aggregates of linear and exponential processes. J. Theoret. Biol. 16, 43 (1967). Authors' address: Peter Sehanzenb~cher, M.D., Abteilung III, Medizinische Klinik, 7400 Tfibingen, W. G e r m a n y
