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COMPARISON OF VOLUME AND SURFACE MECHANISMS FOR MAGNETIC FILTRATION OF
BLOOD CELLS
M. Graham
To cite this version:
M. Graham. COMPARISON OF VOLUME AND SURFACE MECHANISMS FOR MAGNETIC FILTRATION OF BLOOD CELLS. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-779-C1- 784. �10.1051/jphyscol:19841159�. �jpa-00223632�
JOURNAL DE PHYSIQUE
Colloque Cl, supplement au no 1, Tome 45, janvier 1984 page C1-779
COMPARISON OF VOLUME AND SURFACE MECHANISMS FOR MAGNETIC FILTRATION OF BLOOD CELLS
M.D. Graham
CouZter BiomedieaZ Research Corporation, Concord, Massachusetts 01 742, U.S.A.
Rdsumd - Des Qrythrocytes contenant de 1'hBmoglobine diamagndtique ont dt6 mag- ndtiquement filtrss d'une solution sanguine entisre en mettant en oeuvre une approche nouvelle. Celle-qi est fondde sur un mgcanisme de magndtisation cel- lulaire par fixation en surface de chelates lantanide paramagn6tique et soluble L'dfficacitB d'une filtration contenant une dilution de 40mM en concentration chelatee d'erbium ou de dysprosium a 6td comparde avec celle d'une filtration obtenue par paramagnltisation d'hdmoglobine Brythrocytique interne. Les r6sul- tats ont dBmontrd une efficacitd supdrieure dans le premier cas, pour des con- ditions de filtration non-saturde dquivalentes. En consdquence, il apparaft maintenant possible d'obtenir des efficacitds de filtration utile 2 des niveaux dlintensitB et P des gradients de champ magndtique qui se sont dans le pass6 avdrds inefficaces.
Abstract - Erythrocytes containing diamagnetic hemoglobin were magnetically filtered from diluted whole blood via a new mechanism involving cellular magne- tization through surface binding of soluble paramagnetic lanthanide chelates.
Filtration efficiencies for diluents containing 40mM concentrations of erbium or dysprosium chelates are compared to those obtained by paramagnetization of internal erythrocytic hemoglobin and shown to be significantly greater, for equivalent non-saturated filtration conditions. As a consequence, useful fil- tration efficiencies can be reached at field strengths and gradients previously ineffective.
Erythrocytes are unique among mammalian cells in that 95% of their dry mass is a pro- tein (hemoglobin, Hb) containing four Fe atoms per molecule. Although attempts were made to isolate erythrocytes through the effects of magnetic fields on Hb iron (1,2), practical separations had to await development of high-gradient magnetic filtration
(HGMF). Separations have now been achieved through several mechanisms, all involving paramagnetization of the intracellular Hb (3-6). Because the concentration of cellu- lar Hb is set by physiologic considerations and its total amount is limited by cellu- lar volume, magnetic contrasts possible with these erythrocyte-specific mechanisms require intense magnetization fields for useful filtrations. Practically, magnetic filtrations of blood cells would be more attractive if mechanisms capable of greater cellular contrasts were available, so that smaller, less-expensive magnetic systems could be used.
Recently a promising new technique was described in which blood cells containing dia- magnetic Hb were filtered f r ~ m whole blood diluted with a solution of lanthanide che- lates ( 7 , 8 ) . In this non-specific approach, soluble paramagnetic ions are bound to the cellular surface in sufficient amounts to give the cell appreciable magnetic con- trast over its paramagnetic suspending media. The technique causes minimal cellular insult (8), and its dependence on chelate concentration (8) and magnetizing fiePd (7) have been described. Here, efficiencies of magnetic filtrations via surface binding of Er and Dy chelates from 40mM diluents are compared with those resulting via two volume mechanisms based on Hb paramagnetization. Calculations depending from the ex- perimental chelate data predict essentially total filtrations at magnetizing fields of 0.3T, easily attainable with small magnetic circuits.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841159
JOURNAL DE PHYSIQUE
EXPERIMENTAL METHODS
Commercial i s o t o n i c s a l i n e ( I s o t o n 11; C o u l t e r D i a g n o s t i c s ) was used a s b a s e f o r t h e Hb-paramagnetization d i l u e n t s ; a s b u f f e r , disodium hydrogen phosphate ( F i s h e r Scien- t i f i c Co) was added i n r a t i o s of 1.9428 p e r l i t e r f o r o x i d i z i n g s o l u t i o n s i n c l u d i n g 20mM sodium n i t r i t e (Fisher S c i e n t i f i c Co) o r l . l l g p e r gram of sodium d i t h i o n i t e (J.T. Baker Chemical Co) i n t h e lOmM deoxygenating s o l u t i o n s (9). Mixed t h e day of use, paramagnetization d i l u e n t s were vacuum-filtered through 0.45-micron f i l t e r s and had t h e i r pH a d j u s t e d t o 7.0-7.1 by a d d i t i o n of e i t h e r NaOH o r HC1. Owing t o i t s h i g h oxygen r e a c t i v i t y , d i t h i o n i t e was t r a n s f e r r e d and weighed i n flowing n i t r o g e n , and t h e b u f f e r e d s a l i n e used i n deoxygenating d i l u e n t was s a t u r a t e d w i t h n i t r o g e n b e f o r e a d d i t i o n of t h e d i t h i o n i t e . F i l t r a t i o n , pH adjustment, and pre-use s t o r a g e of deoxy- genating d i l u e n t were done under n i t r o g e n .
Because l a n t h a n i d e s p r e c i p i t a t e a t p h y s i o l o g i c pH i n s o l u t i o n s b u f f e r e d by phosphate (or c a r b o n a t e ) , t h e l a n t h a n i d e d i l u e n t s were mixed de novo from phosphate-free s t o c k s o l u t i o n s (8) rpade w i t h i n a week of use. E f f e c t i v e l y , 40mM of Er o r Dy c h l o r i d e hexa- h y d r a t e (Aldrich Chemical Co) was removed from a d e s i c c a t o r and d i s s o l v e d i n a 44mM s o l u t i o n of disodium ethylenediaminetetra-acetic a c i d (disodium EDTA; F i s h e r S c i e n t i - f i c Co) b u f f e r e d t o pH = 7.0-7.1 w i t h 20mM 1,4-piperazinebis(ethane-sulfonic a c i d ) i n f r e e - a c i d form (PIPES; Sigma Chemical Co). Mixing was done i n p l a s t i c glassware, and pH adjustment was w i t h NaOH. Osmolarity of t h e d i l u e n t s was approximately 310mOsm.
To keep d i l u e n t o s m o l a r i t y d i f f e r e n c e s from a f f e c t i n g f i l t r a t i o n r e s u l t s through vol- ume o r shape e f f e c t s , a l l d i l u e n t s were a d j u s t e d t o 310mOsm by a d d i t i o n of.3M NaCl o r d i s t i l l e d water. D i l u e n t s were s t o r e d i n capped p o l y s t y r e n e c u l t u r e f l a s k s u n t i l use.
F i l t r a t i o n d a t a were a c q u i r e d u s i n g d i l u t e d blood from 5 male v o l u n t e e r s . Bloods were drawn by venipuncture i n t o evacuated t u b e s (6451 Vacutainer; Becton-Dickinson) con- t a i n i n g 10.5mg disodium EDTA a s a n t i c o a g u l a n t . The samples were processed w i t h i n s i x hours of drawing and were analyzed (Table 1 ) f o r normalcy (S-Plus C o u l t e r Counter;
C o u l t e r E l e c t r o n i c s , I n c ) p r i o r t o d i l u t i o n . 300111 of each blood were p i p e t t e d from t h e drawing tube (kept on a r o c k e r a t room temperature) i n t o a p o l y s t y r e n e f l a s k con- t a i n i n g 30ml of an experimental d i l u e n t a s needed; f l a s k s were g e n t l y shaken t o g i v e homogeneous c e l l u l q r suspensions b e f o r e samples were removed f o r spectrophotometry o r f i l t r a t i o n . For t h e l a t t e r , l a n t h a n i d e s u s p e n s i o n s were e q u i l i b r a t e d w i t h oxygen.
Hemoglobin c o n s t i t u e n c y of t h e suspended c e l l s was determined by f u r t h e r d i l u t i n g a sample of each suspension t o a f i n a l r a t i o of 1:500 w i t h t h e r e s p e c t i v e d i l u e n t ( t o minimize s c a t t e r i n g e f f e c t s ) and measuring i t s ahsorbances a t 560, 576, and 630nm a g a i n s t t h e c e l l - f r e e d i l u e n t i n a second l.Ocm c u v e t t e a s r e f e r e n c e (Model 575; Cole- man Instrument D i v i s i o n ) . Published e x t i n c t i o n c o e f f i c i e n t s (10) were used t o calcu- l a t e t h e s u s p e n s i o n ' s oxyHb, deoxyHb and metHb c o n c e n t r a t i o n s ; t h e f r a c t i o n of each component was taken a s t h e r a t i o of i t s c a l c u l a t e d c o n c e n t r a t i o n t o t h e sum of con- c e n t r a t i o n s of t h e s e t h r e e Hb s p e c i e s ( 9 ) . A s r e f e r e n c e , c e l l s suspended i n t h e un- modified c o m e r c i a l d i l u e n t were e q u i l i b r a t e d w i t h oxygen by bubbling i t through t h e suspension f o r 10 minutes p r i o r t o spectrophotometry.
F i l t r a t i o n of c e l l s from t h e suspensions was accomplished w i t h t h e HGMF system used p r e v i o u s l y ( 7 , 8 ) . The magnetic f i l t e r , based on a d e s i g n by P a u l ( 6 ) , was a D-shaped chamber 1.4ml i n volume (13m l o n g i n t h e flow d i r e c t i o n and 117mm2 c r o s s - s e c t i o n a l a r e a f o r 6 . 4 m of i t s l e n g t h ) machined i n a 2.5cm x 2.5cm p l a s t i c block 1.25cm t h i c k . The chamber was f i l l e d 15.5% by volume w i t h a mesh woven of 430 s t a i n l e s s s t e e l w i r e 5 0 ~ m i n diameter; i n s o f a r a s p o s s i b l e t h e l o n g e r s i d e of t h e mesh was arranged par- a l l e l t o flow and p e r p e n d i c u l a r t o t h e magnetizing f i e l d . The magnetic f i l t e r was mounted between 5cm p o l e p i e c e s on a lOcm electromagnet (V-4005, w i t h V-2901 supply;
Varian A s s o c i a t e s ) and s u b j e c t e d t o magnetizing f i e l d s a s measured by a H a l l - e f f e c t gaussmeter (Model 615, w i t h HT.Bl-0608 probe; F.W. B e l l , I n c ) . Suspension flows of 0.75ml/min upward through t h e f i l t e r were c o n t r o l l e d by a motor-driven s y r i n g e pump f i t t e d w i t h a 3ml s y r i n g e t o c o n t a i n t h e suspension samples. Magnetic f i l t r a t i o n e f - f i c i e n c i e s were c a l c u l a t e d a s h a s been d e s c r i b e d (7) from c e l l counts (ZB C o u l t e r Counter w i t h C-1000 Channelyzer; C o u l t e r E l e c t r o n i c s , I n c ) made on t h e i n f l u x and e f f l u e n t of t h e f i l t e r ; averaged r e s u l t s f o r t h e 5 donors a r e given i n F i g . 1.
RESULTS AND DISCUSSION
T a b l e 1. S-Plus d a t a f o r t h e f i v e male donors from whose b l o o d s u s p e n s i o n s were made f o r u s e i n f i l t r a t i o n s t u d i e s . M u l t i p l e samples were t a k e n from e a c h d o n o r , t o a l l o w c o m p i l a t i o n of t h e d a t a i n F i g . 1 o v e r s e v e r a l e x p e r i m e n t a l s e s s i o n s . E n t r i e s a r e donor a v e r a g e s , w h i l e t h e Mean ( S t a n d a r d D e v i a t i o n ) v a l u e s a r e f o r a l l samples.
C e l l C o ~ ~ n t Hemoglobin Hematocrit C e l l Volume C e l l Hb C e l l Hb Donor C , x 1 0 ~ / m m ~ Hb, g / d l H c t , % MCV, urn3 MCH, pg MCHC, g / d l
Mean (SD) 5.42(0.23) 15.3(0.5) 47.9(1.9) 88.4(3.0) 2 8 . 3 ( 1 . 3 ) 31.9(0.7)
Spectrophotometry on c e l l s suspended i n oxygenated commercial d i l u e n t i n d i c a t e d t h a t n e a r l y a l l o f t h e c e l l u l a r Hb (0.98 t o 0.99+) was i n t h e oxygenated s t a t e , t h e rest b e i n g met%. F o r c e l l s i n deoxygenating d i t h i o n i t e d i l u e n t , a s i m i l a r d i v i s i o n was s e e n , t h e major component b e i n g deoxyHb. However f o r c e l l s suspended i n o x i d i z i n g n i t r i t e d i l u e n t t h e c o n v e r s i o n was l e s s complete, w i t h 0.93 t o 0.97 of t h e t o t a l Hb c o n t e n t b e i n g c a l c u l a t e d a s met%; t h e remainder u s u a l l y had a s i t s major component oxyHb, a f i n d i n g c o n s i s t e n t w i t h e a r l i e r work ( 9 ) . I n t h e l a n t h a n i d e d i l u e n t s , 0.90 t o 0.97 o f t h e t o t a l Hb was oxyHb, t h e r e s t c a l c u l a t e d t o b e p r e d o m i n a n t l y deoxyHb.
When t h e s e s u s p e n s i o n s were oxygenated by b u b b l i n g , a s was done p r i o r t o t h e i r f i l - t r a t i o n , t h e c a l c u l a t e d oxyHb c o n t e n t i n c r e a s e d t o 0.98-b.
F i l t r a t i o n e f f i c i e n c i e s f o r c e l l s suspended i n t h e f o u r e x p e r i m e n t a l d i l u e n t s a p p e a r i n F i g . 1. Data f o r t h e p a r a m a g n e t i z i n g d i l u e n t s r e f l e c t t h e d i f f e r e n c e s s e e n i n Hb c o n v e r s i o n and may b e compared w i t h e a r l i e r r e s u l t s o b t a i n e d u s i n g t h e same f i l t e r a t a flow r a t e of l.Oml/min and 8% f i l l i n g f a c t o r ( 9 ) . S i m i l a r l y , d a t a f o r t h e l a n t h - a n i d e d i l u e n t s d e m o n s t r a t e t h e a d v a n t a g e i n magnetic moment Dy h a s o v e r Er (10.5 v s . 9.5 Bohr magnetons, r e s p e c t i v e l y ) , a s w e l l a s t h e c l e a r s u p e r i o r i t y b o t h have o v e r t h e p a r a m a g n e t i z i n g d i l u e n t s .
F i g . 1. Magnetic f i l t r a - t i o n e f f i c i e n c i e s f o r hu- man e r y t h r o c y t e s suspended i n two volume-active para- m a g n e t i z i n g d i l u e n t s ( d i - t h i o n i t e and n i t r i t e ) and s u r f a c e - a c t i v e d i l u e n t s c o n t a i n i n g 4OmM E r o r Dy.
The same f i l t e r was u s e d i n a l l d e t e r m i n a t i o n s , a t
0.75ml/min f l o w r a t e . / I 20mM NITRITE
1
3 0 I I I I I I I I I
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
FIELD INTENSITY, T
Cl-782 JOURNAL DE PHYSIQUE
A s e m i - q u a n t i t a t i v e comparison can b e o b t a i n e d through use of t h e f i l t e r e q u a t i o n de- veloped by Watson ( l l ) , ( 1 - E) = exp(-Kx), where E i s t h e magnetic f i l t r a t i o n e f f i c - iency i n p e r c e n t d i v i d e d by 100, x i s t h e r e l a t i v e c e l l u l a r magnetic s u s c e p t i b i l i t y
( o r c o n t r a s t ) , and K i s d e f i n e d by Eq. 1, below. The i n t e n t i s t o c a l c u l a t e K based on t h e experimental f i l t r a t i o n d a t a f o r t h e b e s t - c h a r a c t e r i z e d suspension and t h e n use t h e r e s u l t t o c a l c u l a t e x f o r t h e o t h e r d i l u e n t s .
Mammalian e r y t h r o c y t e s c o n s i s t of a c e l l u l a r membrane s e v e r a l nanometers t h i c k s u r - rounding a n u c l e a r cytoplasm t h a t i s e s s e n t i a l l y Hb (12); t h e i r shape i s a d i s k con- cave on b o t h of i t s f a c e s . I n p h y s i o l o g i c c o n d i t i o n s , human e r y t h r o c y t e s a r e approx- imately 7.7pm i n diameter and 2.8ym i n maximal t h i c k n e s s , t h i n n i n g t o 1.5ym i n t h e i r c e n t r a l r e g i o n (13). Mean c e l l volume (MCV) i s 87pm3 f o r males compared t o 90pm3 f o r females; p e r volume of b l o o d , t h e c e l l count ( C ) , Hb c o n t e n t (Hb) and h e m a t o c r i t
(volume f r a c t i o n of packed e r y t h r o c y t e s , Hct) a r e g r e a t e r i n males, a t 5.4 x 106/mm3, 16.0g/100ml and 47%, r e s p e c t i v e l y . Both s e x e s have average c e l l u l a r Hb c o n t e n t (MCH) of 29pg and Hb c o n c e n t r a t i o n (MCMC) of 35gI100ml. Thus, d a t a i n Table 1 compare w e l l with r e f e r e n c e v a l u e s f o r males, except f o r MCHC which i s s l i g h t l y below t h e normal range of 32-37g/100d. Because c e l l Hb c o n c e n t r a t i o n i s an important parameter i n t h e paramagnetization methods, a l l c a l c u l a t i o n s have been done u s i n g t h e mean v a l u e s l i s t e d i n Table 1; m o l a r i t y of c e l l u l a r Hb i s then 4.95mM, corresponding t o 2.64 x108 Hb molecules p e r e r y t h r o c y t e .
E r y t h r o c y t e s c o n t a i n approximately 95% of t h e i r d r y mass a s Hb ( e . g . , 1 4 ) s o t h a t t h e average dry mass h e r e i s 2 9 . 8 p g I c e l l . Given an average e r y t h r o c y t i c d e n s i t y p = 1.096 g/cc, t h e t o t a l c e l l mass i s 9 7 p g / c e l l , l e a v i n g 6 7 p g / c e l l a s w a t e r (75.9% by volume).
Assuming t h a t Hb (p = 1.335gIcc; 1 5 ) and t h e r e s i d u a l d r y mass d i f f e r l i t t l e i n den- s i t y , 28.3pg of Hb o c c u p i e s about 22.9% by volume o f each c e l l . The volume f r a c t i o n s can 'be combined w i t h published s u s c e p t i b i l i t y d a t a t o p r o v i d e e s t i m a t e s of l i m i t i n g c e l l u l a r magnetic s u s c e p t i b i l i t i e s under t h e v a r i o u s experimental c o n d i t i o n s . Heme- molar s u s c e p t i b i l i t i e s XM a r e 11,910 x lod6 cgs/mol (16) and 2460 x cgs/mol ( 1 7 ) , r e s p e c t i v e l y f o r human Hb i n r h e deoxygenated and oxygenated s t a t e s ; a s i m i l a r v a l u e was n o t found f o r m e t % , s o XH = 13,875 x 10-6 cgs/mol f o r bovine met% a t pH = 7.05 h a s been used (18). These v a l u e s g i v e expected c e l l u l a r s u s c e p t i b i l i t i e s of -3.88, -7.94 and -3.57 x 10-6 MKSu f o r c e l l s c o n t a i n i n g deoxyHb, oxy% and metHb, respec- t i v e l y , when t h e above volume f r a c t i o n s a r e used and it i s assumed t h a t a l l c e l l u l a r Hb is i n a s i n g l e form and t h a t diamagnetic m o i e t i e s e q u a l w a t e r i n s u s c e p t i b i l i t y . Watson's e q u a t i o n assumes s p h e r i c a l p a r t i c l e s t r a v e r s i n g a t low flow r a t e a f i l t e r c o n t a i n i n g only a few p e r c e n t by volume of m a t r i x m a t e r i a l . The e r y t h r o c y t i c geome- t r y and t h e 15.5% f i l l i n g f a c t o r used i n t h e s e experiments both f a i l t o meet assumed c o n d i t i o n s ; f u r t h e r , both paramagnetization d i l u e n t s may f a i l t o t o t a l l y convert a l l c e l l u l a r Hb o r produce Hb d e g r a d a t i o n products t h a t may not b e paramagnetic. D i l u e n t o s m o l a r i t i e s were s t a n d a r d i z e d t o c o n t r o l e r y t h r o c y t i c volume (and s h a p e ) , and t h e i r formulation was s e l e c t e d t o g i v e r e l i a b l e Hb conversion w i t h o u t d e t e c t a b l e Hb degra- t i o n ( 9 ) . Under t h e s e c o n d i t i o n s i t seems p e r m i s s i b l e t o w r i t e K' = xK, where ris
a dimensionless f a c t o r intended t o account f o r t h e non-spherical shape of t h e c e l l s and t h e h i g h e r f i l l i n g f a c t o r of t h e f i l t e r m a t r i x . Then, f o r
F = f i l l i n g f a c t o r of f i l t e r = 0.155 L = e f f e c t i v e f i l t e r l e n g t h = l . l l c m
K = nMq?oHn = K' Ix (1)
a = r a d i u s of m a t r i x w i r e = 25ym 9saLrlvo R Ms = w i r e s a t u r a t i o n magnetization
= 1 . 5 x l o 5 A/m
Ho = magnetizing f i e l d ( 1 - E) = exp(-Kx) (2)
yo = p e r m e a b i l i t y c o n s t a n t V = c e l l volume, MCV = 88.4ym3 R = c e l l r a d i u s = 3.85ymC
x = c e l l magnetic c o n t r a s t x = - l n ( l - E)/K ( 3 4
q = v i s c o s , i t y of d i l u e n t
vo = suspension v e l o c i t y (= 0.0149cm/sec) x = - l n ( l - E ) / K ' = xC - xd (3b)
xc = s u s c e p t i b i l i t y of c e l l xd = s u s c e p t i b i l i t y of d i l u e n t .
Of t h e parameters l i s t e d , f o u r (Ho, vo, n , X) a r e f u n c t i o n s of t h e p r o t o c o l , t h e re- maining ones b e i n g d e f i n e d by p r o p e r t i e s of e i t h e r t h e f i l t e r o r t h e c e l l s . F i g . 1 was compiled by s e l e c t i n g Ho a t a volume flow of 0.751nl/min f o r a l l d e t e r m i n a t i o n s ;
f o r t h e f i l t e r c r o s s - s e c t i o n a l a r e a of 117mm2, t h i s f l o w r a t e corresponds t o a mean flow v e l o c i t y through t h e f i l t e r of 0.0149cm/sec = vo. I n Big. 1, non-saturated com- p a r i s o n s can b e made a t a magnetizing f i e l d of 0.3T f o r d i l u e n t s c o n t a i n i n g Dy, E r , and d i t h i o n i t e ; t h e l a t t e r can b e s i m i l a r l y compared w i t h t h e n i t r i t e o x i d i z i n g d i l u - e n t a t a f i e l d of 0.4T. Since t h e d i t h i o n i t e d i l u e n t i s b e l i e v e d t o b e t h e most r e - p e a t a b l e of t h e two paramagnetizing d i l u e n t s (91, K' w i l l b e c a l c u l a t e d u s i n g Eq. 3b, t h e experimental d a t a , and t h e s u s c e p t i b i l i t y f o r deoxygenated c e l l s , -3.88 x
A t 0.3T, E = 0.374, g i v i n g K' = 9.06 x l o 4 ; t h i s corresponds t o c o n t r a s t s (MKSu) of 25.9 x f o r Er (E = 0.904) and 34.5 x f o r Dy (E = 0.956). A t 0.4T, t h e de- oxygenated and n i t r i t e - t r e a t e d c e l l s gave f i l t r a t i o n e f f i c i e n c i e s of 0.716 and 0.495 r e s p e c t i v e l y , l e a d i n g t o K' = 2.44 x lo5 f o r t h e f i r s t and a c o n t r a s t of 2.81 x f o r t h e l a t t e r . These v a l u e s assume t h a t t h e s u s c e p t i b i l i t y of t h e paramagnetization d i l u e n t s i s e s s e n t i a l l y t h a t of w a t e r , xw = -9.05 x and t h a t t h e v i s c o s i t y of t h e d i l u e n t s approximates t h a t of i s o t o n i c s a l i n e , rl = 1.019cp. A rough check on a l l assumptions i s provided by t h e c e l l u l a r s u s c e p t i b i l i t y of t h e metHb-containing c e l l s , xC = -6.24 x ( c f . -3.57 x c a l c u l a t e d assuming t o t a l Hb conversion).
When t h e system parameters a r e used t o c a l c u l a t e K , t h e r e s u l t s i n d i c a t e t h a t x as- sumes v a l u e s of 2 t o 3.
From t h e CGS molar s u s c e p t i b i l i t i e s of ErC13 and DyC13, XM = +0.0746 and +0.0896 re- s p e c t i v e l y , t h e MKS s u s c e p t i b i l i t i e s of t h e two 40mM d i l u e n t s can b e c a l c u l a t e d a s 0.0375 and 0.0450; t h e s e v a l u e s a r e e s s e n t i a l l y t h e c e l l u l a r s u s c e p t i b i l i t i e s , given t h e s m a l l p e r c e n t a g e s of them t h e c e l l u l a r c o n t r a s t s r e p r e s e n t . Thus, i t appears t h e c h e l a t e s i n t e r a c t s u f f i c i e n t l y w i t h t h e c e l l s t o g i v e t h e l a t t e r e f f e c t i v e s u s c e p t i - b i l i t i e s a t l e a s t two o r d e r s g r e a t e r t h a n t h e r e l a t i v e paramagnetism a t t a i n a b l e w i t h t h e Hb conversion mechanisms (Table 2 ) .
Unlike t h e paramagnetization d i l u e n t s Table 2 . Summary of c e l l u l a r c o n t r a s t s , d i - which achieve t h e i r e f f e c t by a c t i n g l u e n t s u s c e p t i b i l i t i e s , and c e l l u l a r suscept- on t h e e r y t h r o c y t e ' s volume c o n t e n t i b i l i t i e s r e s u l t i n g from c a l c u l a t i o n s based of Hb, t h e l a n t h a n i d e d i l u e n t s do n o t on F i g . 1. A l l v a l u e s a r e i n MKSu, x l o 6 .
impact t h e c e l l u l a r c o n t e n t s . It i s thought t h a t t h e c h e l a t e s bind t o
c e l l u l a r s u r f a c e s , p o s s i b l y through Agent X xd xc
f u r t h e r complexation of t h e l a n t h a -
n i d e ; t h e n e t c e l l u l a r paramagnetic deoxyHb 5.17 -9.05 -3.88 moment t h u s r e q u i r e s t h a t any s u r f a c e metHb 2.81 -9.05 -6.24 a c c r e t i o n of c h e l a t e exceed t h e vol- Er 25.9 +37490 +37515
ume amount of c h e l a t e excluded by t h e Dy 34.5 +45030 +45065
membrane. For normal human e r y t h r o - c y t e s t h e s u r f a c e a r e a (13) i s about 130ym2 and t h e average volume f o r t h e
c e l l s h e r e i s 88.4ym3. Thus, each c e l l excludes about 2.13 x lo9 molecules of t h e 40mM c h e l a t e i n t h e s e d i l u e n t s and must t h e r e f o r e surface-bind s l i g h t l y more, about 1.64 x 10' chelates/ym2 f o r uniform d i s t r i b u t i o n .
Human e r y t h r o c y t e s have been shown t o b e macropolyanions p o s s e s s i n g about lo7 i o n i c groups p e r c e l l , of which more t h a n 60% a r e t h e carboxyl group of N-acetylneuraminic a c i d , t h e remainder thought t o i n c l u d e some a-carboxyl groups on amino a c i d s (19).
I f i t is assumed t h a t each a n i o n i c s i t e b i n d s a s i n g l e c h e l a t e molecule, about 200 times t h e a v a i l a b l e s i t e s a r e r e q u i r e d t o produce t h e c a l c u l a t e d b i n d i n g d e n s i t i e s . This s u g g e s t s t h a t i n d i v i d u a l s i t e s b i n d m u l t i p l e c h e l a t e s , t h a t s i t e s n o t i d e n t i - f i e d by t h e u s u a l marking methods become involved i n c h e l a t e b i n d i n g , o r t h a t s i t e s normally c o v e r t a r e exposed by t h e experimental d i l u e n t s . The b i n d i n g mechanism i s n o t y e t understood, although i t i s thought t o e s s e n t i a l l y s a t u r a t e a t c o n c e n t r a t i o n s of 10-15mM f o r e i t h e r Er o r Dy (7); f o r l O m M E r , c a l c u l a t i o n s s i m i l a r t o t h e above p r e d i c t t h a t lo8 b i n d i n g s i t e s should g i v e f i l t r a t i o n e f f i c i e n c i e s comparable t o d i - t h i o n i t e , w h i l e i n f a c t e f f i c i e n c i e s c o n s i d e r a b l y g r e a t e r a r e observed (7). This r e - s u l t f u r t h e r s u p p o r t s involvement of more t h a n t h e u s u a l a n i o n i c membrane s i t e s .
C 1-784 JOURNAL DE PHYSIQUE
F i n a l l y , i t s h o u l d b e n o t e d t h a t a l l c o r r e c t i o n s f o r d i a m a g n e t i c m o i e t i e s have been n e g l e c t e d i n t h e s e c a l c u l a t i o n s , i n c l u d i n g t h a t f o r t h e oxygenated Hb c o n t a i n e d i n t h e c h e l a t e - b i n d i n g c e l l s . F u r t h e r , s t a t e d m o l a r v a l u e s a r e l i k e l y t o o v e r - e s t i m a t e a c t u a l d i l u e n t c o n t e n t o f t h e l a n t h a n i d e s o r d i t h i o n i t e , t h e f i r s t b e i n g h y d r o s c o p i c and t h e second b e i n g b o t h impure i n t h e as-purchased s t a t e and l i a b l e t o combine w i t h oxygen (and s o b e r e n d e r e d l e s s e f f e c t i v e ) d u r i n g i t s s t o r a g e and h a n d l i n g .
CONCLUSION
F i l t r a t i o n e f f i c i e n c i e s f o r e r y t h r o c y t e s d i l u t e d w i t h two volume-active paramagneti- z a t i o n d i l u e n t s h a v e been compared w i t h t h o s e f o r c e l l s from t h e same donors s u b j e c - t e d t o e x p e r i m e n t a l s u r f a c e - a c t i v e d i l u e n t s c o n t a i n i n g l a n t h a n i d e c h e l a t e s . The r e - s u l t s show a c l e a r a d v a n t a g e f o r t h e l a t t e r . c a l c u l a t i o n s p i v o t i n g on t h e f i l t r a t i o n system c h a r a c t e r i s t i c a s d e t e r m i n e d f o r deoxygenated c e l l s i n d i c a t e t h a t t h e l a n t h a - n i d e s E r and Dy g i v e c e l l u l a r magnetic c o n t r a s t s (MKSu, x l o 6 ) o f 25.9 and 3C.5, re- s p e c t i v e l y , compared t o 5.17 f o r t h e deoxygenated cells and 2.81 f o r c e l l s c o n t a i n i n g metHb. These c o n t r a s t s o b t a i n d e s p i t e t h e c e l l s b e i n g suspended i n a h i g h l y paramag- n e t i c f l u i d , l e a d i n g t o e f f e c t i v e c e l l u l a r s u s c e p t i b i l i t i e s g r e a t e r by a t l e a s t two o r d e r s t h a n f o r c e l l s whose Hb h a s b e e n c o n v e r t e d by t h e p a r a m a g n e t i z a t i o n mechanisms.
The improved f i l t r a t i o n e f f i c i e n c i e s a t t a i n a b l e w i t h t h e s u r f a c e - a c t i v e d i l u e n t s p e r m i t s u s e f u l f i l t r a t i o n e f f i c i e n c i e s a t f i e l d s a s low a s 0.3T, f i e l d s t r e n g t h s i n - c o m p a t i b l e w i t h h i g h - e f f i c i e n c y f i l t r a t i o n s by t h e p a r a m a g n e t i z a t i o n mechanisms. For example, i f t h e flow r a t e were t o b e reduced t o one-half t h e v a l u e used i n t h e s e ex- p e r i m e n t s , Eq. 3b p r e d i c t s t h a t e i t h e r Dy o r ET would p e r m i t f i l t r a t i o n o f a t least 98% of t h e c e l l s a t 0.3T m a g n e t i z i n g f i e l d . It i s t h i s p r o s p e c t , o f a c h i e v i n g prac- t i c a l f i l t r a t i o n s u s i n g f i e l d i n t e n s i t i e s a v a i l a b l e from compact magnet a s s e m b l i e s , t h a t i s g r e a t l y a t t r a c t i v e .
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