Finite element simulation of the intramyocardial coronary
circulation
Citation for published version (APA):
Huyghe, J. M. R. J., Oomens, C. W. J., Campen, van, D. H., Arts, M. G. J., & Heethaar, R. M. (1988). Finite
element simulation of the intramyocardial coronary circulation. In Computers in cardiology : IEEE conference :
proceedings, vol. 14, 1987, Leuven, Belgium / Ed. K.L. Ripley (pp. 335-338). Institute of Electrical and
Electronics Engineers.
Document status and date:
Published: 01/01/1988
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t a r c o m p a r t m e n t s , n o r b e t w e e n intravascu.lar and e x t r a v a s c u l a r s p a c e . T h e p a s s . i v e p.óp.ÀË o f t h e m y o c a r d i a l t i s s u e a r e d e s c r i b e d tjv àn áriÈotropic q u a s i , - l i h e a r v i s c o e 1 a s t - i c l a w . T h " e p a r i m e t e r s of t h e l a w a r e d e r i v e d f r o m experimental data of s e v e r a l a u t h o r s 2 , 3 , 4 . A t i m e , s t r a . i n a n d strain r a t e d e p e n d e n t c o n t r a c t i l e fiber stress is srroer_ i p p g : . d , o n t h e p a . s s i v e s t r e s s d u r i n g th" ;y;;ái;; p h a s e . T h e d o w n s t r e a m boundary coriaition ls de s c r i b e d b y a l i n e a r 4 e l e m e n t model of the per.i_ f e r a l c i r c u l a t i o n b o r r o w e d from Westerhof et a.l.5.
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r i m e n t a l d a t a f r o m t h e l i t e r a t u r e 6 , 7 , B , 9 1 t i g . 2 1 . + nil'4 r o nllulr r n l Mr pLV=o V E I N S , , F i g . 5 . ï h e f i n i t e e l e m e n t m e s h o f t h e m o d e l . F i 9 . 4 . M o d e l r e s u l t o f s u b e n d o c a r d i a l in t r a m y o _ c a r d i a l p r e s s u r e d u r i n g a . l e f t v e n t r i c u i a r c o n t r a c t i o n a t p L V = O ( t w o - p h a s e s.imul a _ t t o n ) . ( B ) I M P m a x o L V m a x ' o o o o + + + + a a E N D O E P I F i g . 3 . T r a n s m u r a l e q u a t o r i a l d i s t r i b u t i o n o f i n t r a m y o c a r d i a l p r e s s u r e .
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l a y e r a n d i s c h o s e n a c c o r d i n g to S p a a n l 0 . T h e h i q h s y s t o l i c t r a n s m u r a l p r e s s u r e g r a d Íe n t r e s u l t s i n ' a s i g n i f i c a n t r e d u c t i o n o f a r t e r i a l c o r o n a r y f l o w a n d a s i g n i f i c a n t i n c r e a s e - o f v e n o u s c o r o n a i y f l o w d u r i n g s y s t o l e ( f i g . B ) . T h e s e s t r o n g a i t e r a t i o n o f c o r o n a r y f l o w d u r i n g s y s t o l i c c o n t r á c t i o n a r e p r e d i c t e d b y t h e m o d e l n o t o n l y f o r t h e n o r m a j c a r d i a c c y c l e b u t a l s o d u r i n g c o n -t r a c -t i o n o f a n u n l o a d e d v e n t r i c l e ( l e f t v e n t r i c u -1 a r p r e s s u r e = 0 ) . T h e p o o r - s e n s i t i v i t y o f t h e s y s t o l i c r e d u c t i o n o f a r t e r i a l c o r o n a r y f l o w t o t h e s y s t o l i c i n t r a v e n t r i c u l a r p r e s s u r e i s c o n s i s -t e n -t w i -t h u n p u b l i s h e d e x p e r i m e n t a l d a t a o f R ' K r a m s a n d N . ï , l e s t e r h o f ( F r e e u n i v e r s i t y ' A,msterdam) . u m e p e r u n i t a r t e r i o v e n o u s i n i ti a l b l o o d v o l u m e P e r F i g . 8 . T o t a l c o r o n a r Y p e r f u s i o n m o d e l .
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F i g . 9 s h o w s th e a r t e r i a l c o r o n a r y f l o w p a t t e r n at e n d - d i a s t o l e f o r t h e n o r m a l c J r d i a c bycl e and a f t e r o c c l u s i o n . T h e t o p p a n e l p e r t a i n i t o t h e b a s a l c o n d i t i o n : a r t e r i a l b l o o d f l o w s t h e n f r o m t h e e p i c a r d i a l s u r f a c e i n t o t h e w a l l . ï h e b o t t o m p a n e l p e r t a i n s t o t h e s i t u a t . i o n a f t e r o c c l u s i o n . I l ! h l r c a s e s i g n i f i c a n t c o l l a t e r a l f l o w i s n r p _ d i c t e d a - 1 o n g t h e e p i c a r d i a l p l e x u s f r o m ' i n . - f , á à i _ t n y m u s c l e to t h e i s c h a e m i c m u s c l e . F i g . 9 . R a d i a l a n d a x i a l c o r o n a r y f l o w c o m p o n e n t i n t h e b a s a l s i t u a t i o n ( t o p ) a n d a f t e r o c c l u s i o n ( b o t t o m ) . T h e r a d i a l c o m p a r t m e n t
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f r o m t h e s y m m e t r y a x i s ( o n . É h i s p . i è t u r e : f r o m r i g h t t o l e f t ) a n d t h e a x i a i compo_ n e n t i s p o s . i t i v e f r o m a p e x t o b a s e . C o n c l u s i o n T h e f i n i t e e l e m e n t m e t h o d o p e n s n e w p o s s i b i l i t i e s t o t h e m o d e l I i n g o f t h e c o r o n a r y c i r c u l a t i o n . A l t h o u g h a g r e a t d e a l o f u n c e r t a i n t y r e m a i n s c o n _ c e r n i n g t h e c h o i c e o f t h e p a r a m e t e r i , we can show t h a t t h e m o d e l i s a b l e t o r e f l e c t t e n d e n c i e s w h i c h a r e c o n s i s t e n t w i t h t h e e x p e r i m e n t . R e f e r e n c e s 1 . S t r e e t e r , D . D . J r . , H a n n a , W . T . , E n g i n e e r . i n g m e c h a n i c s o f s u c c e s s i v e s t a t e s i n c a n i n e l e f i v e n t r i c u l a r _ m y o c a r d i u m : II . F i b e r a n g l e a n d s a r " c o m e r e l e n g t h , C i r c . R e s . 3 3 : 6 5 7 _ 6 6 4 , 1 9 7 3 . , -2 . P i n t o , J . G . , F u n g , J . C . , l . 4 e c h a n i c a l p r o p e r t i e s o f t h e h e a r t m u s c l e i n t h e p a s s i v e s t a t e , J . B i o m e c h a n i c s 6 : 5 9 7 - 6 L 6 , 1 9 7 3 . 3 . D e m e r , 1 . L . , Y i n , F . C . p . , p a s s i v e b i a x i a l m e _ c h a n i c a l p r o p e r t i e s o f i s o l a t e d c a n i n e m v o c a r _ d i u m , J . P h y s i o l . 3 3 9 : 6 1 5 - 6 3 0 , 1 9 8 3 . 4 . V a n H e u n i n g e n , R . , R i j n s b u r g e r , W . H . , t e r K e u r s , H . E . D . J . , S a r c o m e r e l e n q t h c o n t r o l i n : l f i a l g g m u s c l e , A m . J . p h y s i o i . 2 4 2 , H 4 1 1 _ 420, 1982. 5 . l ^ l e s t e r h o f , N . , E l z i n g a , G . , v a n d e n B o s , G . C . , I n f l u e n c e o f c e n t r a l a n d p e r i p h e r a l c h a n g e s on t h e h y d r a u l ic i n p u t i m p e d a n c e o f t h e s y ó t e m i c a r t e r i a l t r e e , M e d . B . i o l . E n g . 1 1 : l i O _ l Z _ 2 , 1 9 7 3 . 6 . A r t s , ï . , V e e n s t r a , p . C . , R e n e m a n , R . S . , E p i _ c a r d i a l d e f o r m a t i o n a n d l e f t v e n t r i c u l a r w a l l m e c h a n i c s d u r i n g e j e c t i o n i n t h e d o g , A m . J . P h y s i o l . 2 4 3 , H 3 7 9 - 3 9 0 , 1 9 8 2 . 7 . l ^ I a l d m a n , _ L . K . , F u n q , y . C . , C o v e l l , J . W . , T r a n s r n u r a l m y o c a r d i a l d e f o r m a t i o n in the ca_ n i n e l e f t v e n t r i c l e : n o r m a l i n v . i v o t h r e e _ d i m e n s i o n a l f i n i t e s t r a i n s , C i r c . R e s . 5 7 : ' I 5 2 - 1 6 ? I o a K B . P r i n z e n , f . t i l . , A r t s , T . , v a n d e r V u s s e , G . J . , R e n e m a n , R . S . , F i b e r s h o r t e n i n g i n t h e i n n e r l a y e r s o f t h e l e f t v e n t r i c u l a r w a l l a s a s s e s s -e d f r o m -e p ' i c a r d i a l d -e f o r m a t j o n d u r i n g normoxia a n d i s c h e m i a , J . B i o m e c h . l T : B 0 i _ 8 1 i , 1 9 8 4 . 9 . H e i n e m a n , F . W . , G r a y s o f l , J . , T r a n s m u r a l d . i s -t r i b u -t i o n o f i n -t r a m y o c a r d i a l p r e s s u r e measurec ! y - m j c l g g i p e t t e _ t e c h n i q u e , A m . J . p h y s . i o t . 2 4 9 : H I 2 I 6 - | 2 2 3 , 1 9 8 5 . 1 0 . S p a a n , F : 4 . E . , C o r o n a r y d i a s t o l i c p r e s s u r e -f l o w r e l a t i o n a n d z e r o -f l o w p r e s s u r e e x p l a i n e d o n t h e b a s i s o f i n t r a m y o c a r d i a l c o m p j i a n c e , C i r c . R e s . 5 6 : 2 9 3 - 3 0 9 , i 9 8 5 .
