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Paramagnetic attraction of erythrocyte flow due to an inhomogeneous magnetic field
181
Bioelectrochemistry and Bioenergetics, 30 (1993) 181-188 Elsevier Sequoia S.A., Lausanne
JEC BB 02019
Paramagnetic attraction of erythrocyte flow due to an inhomogeneous magnetic field Takeshi Shiga a*, Masaharu Okazaki b, Akitoshi Seiyama ’ and Nobuji Maeda ’ a Department of Physiology, Medical School, Osaka University, Suita, Osaka 565 (Japan) b Division of Radiation Chemists, Govemmen t Industrial Research Institute, Nagoya 462 (Japan) ‘Department of Physiology, School of Medicine, Ehime University, Ehime 791-02 (Japan)
Abstract
The effect of an external inhomogeneous magnetic field on the flow of erythrocytes containing paramagnetic hemoglobin was studied systematically, with three experimental setups. (1) The attraction of a narrow stream of erythrocyte suspension towards stronger magnetic field, in a wide laminar flow, was found to be proportional to the magnetic susceptibility of erythrocytes ,y, the product of the field strength and its spatial gradient B X d B/dz, and the reciprocal of flow velocity l/v, and also to the hematocrit h of the suspension. (2) A model flow of erythrocyte suspension in the vessel showed a small change in the radial distribution of erythrocytes arising from a magnetic field, which is proportional to x, B X d B/d z (up to 20 T’/m), l/v, and h ( < 5%). However, the attraction saturates at high values of B XdB/dz and h. (3) Acceleration of the sedimentation rate was detected for paramagnetic etythrocytes in an inhomogeneous magnetic field, but not with diamagnetic erythrocytes. In short, the paramagnetic attraction takes place with venous blood, and depends on the product of the field strength and its spatial gradient, the degree of deoxygenation, the flow velocity, and the hematocrit.
INTRODUCTION
An external magnetic field may affect the blood flow by way of three mechanisms. Firstly, magnetohydrodynamic action, which is predicted to decrease the aortic flow velocity by 10% in a uniform magnetic field of ca. 5 T [l], but no
* To whom correspondence 0302-4598/93/$06.00
should be addressed.
0 1993 - Elsevier Sequoia S.A. All rights reserved
182
experimental proof is given. Secondly, diamagnetic anisotropic interaction, which modifies the orientation of flowing erythrocytes, either with sickled cells at homogeneous 0.35 T [2,3] or with normal discocytes at several tesla [4]. Thirdly, paramagnetic interaction, which acts only on the paramagnetic erythrocytes in fields of around 1 T with a strong spatial gradient, as applied to magnetic separation [5,6]. In this study we have concentrated our interest on the paramagnetic interaction between blood flow and inhomogeneous magnetic fields, as reported recently [7-91. In order to investigate the magnetic attraction of the blood component, erythrocytes are of particular interest because we can modify their magnetic susceptibility by changing the spin state of hemoglobin. As will be shown later, the deoxygenated erythrocytes are paramagnetic and magnetically attracted, while the oxygenated erythrocytes are diamagnetic and not attracted; and the erythrocytes containing high- and low-spin methemoglobin differ in their magnetic susceptibilities. We have already demonstrated the magnetic attraction of paramagnetic erythrocytes, using three experimental procedures: (1) displacement of a narrow stream line of erythrocyte suspension in a wide laminar flow [7,8]; (2) a small change in the distribution of erythrocytes flowing through a cylindrical vessel [9]; (3) an acceleration of the erythrocyte sedimentation rate [lo], due to an inhomogeneous magnetic field. This paper summarizes our results with some new data, in the form of a mini review. We demonstrate here the paramagnetic interaction between blood flow and the magnetic field - i.e. the attraction of paramagnetic erythrocytes by an inhomogeneous magnetic field. MATERIALS AND METHODS
Materials
Four types of erythrocytes, with different spin states of hemoglobin, were prepared from freshly drawn human blood after removal of plasma and buffy coat [7-101. The erythrocytes were suspended in isotonic buffered saline (90 mM NaCI, 5 mM KCl, 50 mM Na phosphate and 5.6 mM glucose at pH 7.4) after washing and were prepared as follows. (1) erythrocytes with oxygenated hemoglobin; (2) erythrocytes deoxygenated by treating with sodium hydrosulfite; (3) after oxidizing the hemoglobin to methemoglobin with sodium nitrite (20 mM), the erythrocytes were washed and resuspended at pH 5.7 to establish the high-spin ferric state of methemoglobin; (4) erythrocytes treated with potassium cyanide (10 times the total heme) and washed with a buffer at pH 7.4 to obtain the low-spin state of methemoglobin.
183 (a)
(b)
Fig. 1. Flow channels and sedimentation tube, in the inhomogeneous magnetic field. (al For observation of the displacement of an erythrocyte stream line in a iaminar flow [7,8]. The dimension of the channel was 4~0.4~ 150 mm, and the width of the stream line (shown by the dotted line) was ca. 80 pm. (b) For detection of excess flow of erythrocytes to the side branch 191.The inner diameter of the main cylinder was 2.0 mm and that of the side branch 1.0 mm. Cc) Measurement of the erythrocyte sedimentation rate [lo]; the blood suspension was packed in a Westergren tube (inside diameter 2.5 mm). The inhomogeneous magnetic field was generated from an electromagnet and an iron block with one side tapered, to which the channels and the tube were tightly attached. The magnetic flux density around the model channel was measured point by point with a gauss meter, then the spatial gradient and the “averaged” value of the product, B X d B/dz, were calculated [8,9].
Flow channels
An inhomogeneous magnetic field was produced with an electromagnet and a triangular iron block attached to a surface of the magnet. Two flow channels were employed. Figure l(a) shows a rectangular flat cell (4 X 150 X 0.4 mm microslide, Vitro Dynamics, NJ) used to establish a wide laminar buffer flow, containing a narrow stream line (ca. 80 pm) of erythrocyte suspension. The displacement of the stream line due to the paramagnetic attraction was observed by microscopic photography [7,8]. Figure l(b) shows a glass cylinder (outside diameter 4.0 mm, inside diameter 2.0 mm) with a side branch from which a small portion of the erythrocyte flow was taken to detect small changes in the distribution of flowing erythrocytes. The increase of erythrocytes due to the paramagnetic attraction was quantified by the determination of hemoglobin concentration. Figure l(c) shows how erythrocyte sedimentation rate was measured with a Westergren glass tube, placed upright along the iron block [lo]. RESULTS AND DISCUSSION
Displacement of erythrocyte stream line in laminar flow (781
Using the flow channel shown in Fig. l(a), the position of the narrow stream line was measured on microscopic photographs before and during the application of the magnetic field, and the displacement of the stream line due to magnetic attraction was obtained by comparing the two values. Figure 2 shows the displacement of the stream line of erythrocyte suspension, whose diameter is ca. 80 pm in the wide laminar flow (Fig. l(a)). The displacement is detected only for paramagnetic erythrocytes, and not for oxygenated erythrocytes containing diamagnetic
a4
I
ra3
E
(‘I
L!!
!a2
,D
ep
5
0 at
0
10
20 30
40
Mvp =
g
LO
Lo4
5
E0.s ::
0 ff
fd’
/* SL
a4
Bat
0’ 0
5
IO
IS
Harmtwit/%
Fig. 2. Displacement of the etythrocyte stream line as functions of (a) the product of the magnetic flux density and its gradient, (b) the square of the magnetic moment of iron in hemoglobin, which is proportional to the magnetic susceptibility, Cc)flow velocity, and Cd)hematocrit value of the etythrocyte stream. Standard experimental conditions unless specified: flow velocity 0.7 mm/s, average value of B XdB/dz 29 T’/m. For erythrocytes containing high-spin methemoglobin (hematocrit of 6%), containing high-spin methemoglobin (S = 5/2) (m), low-spin methemoglobin (S = l/Z) (01, deoxy-hemoglobin (S = 2) (01, and oxy-hemoglobin (S = 0) (a). Standard deviations are smaller than the symbol size. (For details, see refs. 7 and 8).
oxyhemoglobin. The displacement became larger with the increase of: (1) the product of the magnetic field strength and its spatial gradient; (2) the magnetic susceptibility of hemoglobin in erythrocytes; (3) the reciprocal of the flow velocity; (4) the hematocrit of the suspension. The forces acting on a flowing paramagnetic particle are I;;n_ and F, which are now described. The force F_ is due to attractive magnetic interaction. Neglecting the Lorentz force and the induced Hall effect (because they are small) F,,=,I&L-r(B,xdB,/dz) where x is the paramagnetic susceptibility of the material, V the volume, B, and dB,/dz the magnetic flux density and its gradient in the z coordinate (z is the direction of the magnetic attraction), and ,U is the magnetic permeability. The frictional Stokes force Ff gives resistance for the displacement
185
where u is the velocity of displacement, and R the hydrodynamic radius of the moving particle in a medium of viscosity q. Ff is equilibrated to Fmg within a short time. From these tivo equations, the velocity of displacement u is obtained, and by integrating u along the path (y axis) the estimate of displacement L can be calculated: L = k=u dr = jYzFm,$(6~~~Rv)
dy = V,y/(6mjpRv)
Yl
x jY*Bz(dBz/dr)
dy
Yl
where y, and yz are the y coordinates of the particular erythrocytes at t = 0 and at t = T when the observation was made, respectively, and u is the flow velocity (y direction); thus dt = dy/v. Although the displacement of the erythrocyte stream line occurred in accordance with the above theory, the observed displacement is much larger than the calculated value for a single erythrocyte. Moreover, the displacement depended on the ‘hematocrit of the erythrocyte suspension (Fig. 2(d)). These results show that a group of erythrocytes (in a “volume”) is attracted as a whole by the magnetic force, by this experimental arrangement, as discussed previously [8]. Asymmetric distribution of jlowing erythrocytes in a vessel The attraction of erythrocytes by a strong inhomogeneous magnetic field has been observed [9] with the setup shown in Fig. l(b). A similar flow channel was tested for the separation of paramagnetic (malaria infected) erythrocytes in human blood by Heidelberger et al. in 1946 [ll], but that trial was unsuccessful because the magnetic field strength was too low. In order to separate paramagnetic cells from blood, an extremely high gradient magnetic field is needed [5,6,121. As we have already shown, with paramagnetic erythrocytes containing the high-spin methemoglobin, the proportion of erythrocytes skimmed into the side branch of the flow channel of Fig. 1 (b) is increased by magnetic attraction [9]. The degree of attraction increases linearly with the magnetic susceptibility of erythrocytes, with the product of magnetic field strength and its spatial gradient (but it saturated above ca. 20 T2/m) and with the reciprocal of the flow velocity. Further, a hematocrit dependence was found with maximal attraction at hematocrit readings of ca. 5%, while at 45% no attraction was detected. In the case of mixed suspensions containing erythrocytes with high-spin methemoglobin (paramagnetic) and oxygenated erythrocytes (diamagnetic), the attraction reached a maximum at the “partial hematocrit” for the paramagnetic erythrocytes of ca. 5% and remained nearly constant with further increases of “partial hematocrit” [91. In order to quantify the degree of the magnetic attraction of deoxygenated erythrocytes, we have to measure anaerobically the amount of erythrocytes skimmed into the side branch. Therefore, a spectrophotometer with long optical fiber was attached at the rectangular side branch just below the magnetic field, to take
186
Fig. 3. Excess flow of erythrocytes into the side branch as functions of (a) the product of the magnetic flux density and its gradient, (b) the square of the magnetic moment of iron in hemoglobin, which is proportional to the magnetic susceptibility, (c) flow velocity, and (d) hematocrit value of the erythrocyte suspension. Standard experimental condition unless specified: flow velocity 2.5 mm/s, average value of B xdB/dz 60 T’/m. For erythrocytes (hematocrit of 5%), containing high-spin methemoglobin (S = 5/2) (ml, low-spin methemoglobin (S = l/2) (01, deoxyhemoglobin (S = 2) CO), and oxyhemoglobin (S = 0) (0). The data are shown with standard deviation (bars).
difference spectra before and after exposure to the magnetic field. The changes for the skimmed erythrocytes AV are defined as AV- (amount with field)/(amount without field) - 1. Figure 3 shows the results. AV increased in proportion to the product of the magnetic field strength and its spatial gradient, but saturated at weak magnetic fields (20 T’/m) (Fig. 3(a)). AV also increased in proportion to the magnetic susceptibility of hemoglobin derivatives in the erythrocytes (Fig. 3(b)), and the reciprocal of the flow velocity (Fig. 3(c)). The effect is maximal at an optimal hematocrit of ca. 5% (Fig. 3(d)). Further, Al/ varied with the degree of deoxygenation, in proportion to the estimated magnetic susceptibility. These phenomena can be interpreted as arising from the asymmetric distribution of flowing erythrocytes, made by their paramagnetic interaction with the magnetic field in the cylindrical vessel. The saturation phenomena, at high magnetic field and/or at high hematocrit, may arise from collisions between erythrocytes and collisions with the vessel wall, which form local eddy currents and turbulent flow, and which destroy the magnetic field-induced asymmetry in the distribution. Therefore, as the collision rate increases with increasing the magnetic
187
field and/or the hematocrit, apparently suppressed. Acceleration
of erythrocyte
the magnetic
sedimentation
effect (asymmetric
distribution)
is
rate [lOI
The sedimentation rate of paramagnetic erythrocytes in a Westergren tube increased in a spatially inhomogeneous magnetic field, while no magnetic effect was detected with diamagnetic erythrocytes. This phenomenon is similar to the so-called Boycott effect [13], i.e. the accelerated sedimentation in an inclined cylinder or channel [14]. However, the detailed mechanism of this effect is not fully understood. CONCLUSION
The effect of an external inhomogeneous magnetic field on the flow of erythrocytes containing paramagnetic hemoglobin was studied systematically, with three experimental setups. The results obtained are summarized below. (1) Paramagnetic erythrocytes are attracted by an inhomogeneous magnetic field. (2) The degree of attraction is proportional to (a) the product of magnetic field strength and its spatial gradient, (b) the magnetic susceptibility of hemoglobin, and (c) the reciprocal of the flow velocity. The attraction is detectable with model flow channels in an inhomogeneous magnetic field of above 10 T2/m. (3) The degree of attraction depends on the hematocrit reading, with maximum at ca. 5%. (4) The asymmetric distribution of venous, deoxygenated blood flow in an inhomogeneous magnetic field of above 100 T2/m may induce some biological effect. ACKNOWLEDGMENT
This work was supported in part by grants from the Ministry of Education, Science and Culture of Japan, Nissan Science Foundation, and Ehime Health Foundation. References 1 I.I.H. Chen and S. Saha, J. Bioelectricity, 3 (1984) 293. 2 M. Murayama, Nature, 206 (1965) 420. 3 A.S. Brody, M.P. Sorette, C.A. Gooding, J. Listerud, M.R. Clark, W.C. Mentzer, T.L. James, Invest. Radio]., 20 (1985) 560. 4 A. Yamagishi, T. Takeuchi, T. Higashi and M. Date, Physica B, 177 (1992) 523. 5 D. Melville, F. Paul and S. Roath, Nature, 255 (1975) 706. 6 E.H. Dunlop, W.A. Feiler and M.J. Mattione, Biotech. Advs., 2 (1984) 63. 7 M. Okazaki, N. Maeda and T. Shiga, Experientia, 42 (1986) 842.
R.C. Brasch
and
188 8 9 10 11 12 13 14
M. Okazaki, N. Maeda and T. Shiga, Eur. Biophys. J., 14 (1987) 139. M. Okazaki, K. Kon, N. Maeda and T. Shiga, Physiol. Chem. Phys. Med. NMR, 20 (1988) 3. M. Okazaki, A. Seiyama, K. Kon, N. Maeda and T. Shiga, J. Colloid Interface Sci., 146 (1991) 590. M. Heidelberger, M.M. Meyer and C.R. Damarest, J. Immunol., 52 (1946) 325. J.A. Oberteuffer, IEEE Trans. Magn., 9 (1973) 303. A.E. Boycott, Nature, 104 (1920) 532. K. Abe, Y. Takano and S. Oka, Biorheology, 23 (1986) 17.
Bioelectrochemistry and Bioenergetics, 30 (1993) 181-188 Elsevier Sequoia S.A., Lausanne
JEC BB 02019
Paramagnetic attraction of erythrocyte flow due to an inhomogeneous magnetic field Takeshi Shiga a*, Masaharu Okazaki b, Akitoshi Seiyama ’ and Nobuji Maeda ’ a Department of Physiology, Medical School, Osaka University, Suita, Osaka 565 (Japan) b Division of Radiation Chemists, Govemmen t Industrial Research Institute, Nagoya 462 (Japan) ‘Department of Physiology, School of Medicine, Ehime University, Ehime 791-02 (Japan)
Abstract
The effect of an external inhomogeneous magnetic field on the flow of erythrocytes containing paramagnetic hemoglobin was studied systematically, with three experimental setups. (1) The attraction of a narrow stream of erythrocyte suspension towards stronger magnetic field, in a wide laminar flow, was found to be proportional to the magnetic susceptibility of erythrocytes ,y, the product of the field strength and its spatial gradient B X d B/dz, and the reciprocal of flow velocity l/v, and also to the hematocrit h of the suspension. (2) A model flow of erythrocyte suspension in the vessel showed a small change in the radial distribution of erythrocytes arising from a magnetic field, which is proportional to x, B X d B/d z (up to 20 T’/m), l/v, and h ( < 5%). However, the attraction saturates at high values of B XdB/dz and h. (3) Acceleration of the sedimentation rate was detected for paramagnetic etythrocytes in an inhomogeneous magnetic field, but not with diamagnetic erythrocytes. In short, the paramagnetic attraction takes place with venous blood, and depends on the product of the field strength and its spatial gradient, the degree of deoxygenation, the flow velocity, and the hematocrit.
INTRODUCTION
An external magnetic field may affect the blood flow by way of three mechanisms. Firstly, magnetohydrodynamic action, which is predicted to decrease the aortic flow velocity by 10% in a uniform magnetic field of ca. 5 T [l], but no
* To whom correspondence 0302-4598/93/$06.00
should be addressed.
0 1993 - Elsevier Sequoia S.A. All rights reserved
182
experimental proof is given. Secondly, diamagnetic anisotropic interaction, which modifies the orientation of flowing erythrocytes, either with sickled cells at homogeneous 0.35 T [2,3] or with normal discocytes at several tesla [4]. Thirdly, paramagnetic interaction, which acts only on the paramagnetic erythrocytes in fields of around 1 T with a strong spatial gradient, as applied to magnetic separation [5,6]. In this study we have concentrated our interest on the paramagnetic interaction between blood flow and inhomogeneous magnetic fields, as reported recently [7-91. In order to investigate the magnetic attraction of the blood component, erythrocytes are of particular interest because we can modify their magnetic susceptibility by changing the spin state of hemoglobin. As will be shown later, the deoxygenated erythrocytes are paramagnetic and magnetically attracted, while the oxygenated erythrocytes are diamagnetic and not attracted; and the erythrocytes containing high- and low-spin methemoglobin differ in their magnetic susceptibilities. We have already demonstrated the magnetic attraction of paramagnetic erythrocytes, using three experimental procedures: (1) displacement of a narrow stream line of erythrocyte suspension in a wide laminar flow [7,8]; (2) a small change in the distribution of erythrocytes flowing through a cylindrical vessel [9]; (3) an acceleration of the erythrocyte sedimentation rate [lo], due to an inhomogeneous magnetic field. This paper summarizes our results with some new data, in the form of a mini review. We demonstrate here the paramagnetic interaction between blood flow and the magnetic field - i.e. the attraction of paramagnetic erythrocytes by an inhomogeneous magnetic field. MATERIALS AND METHODS
Materials
Four types of erythrocytes, with different spin states of hemoglobin, were prepared from freshly drawn human blood after removal of plasma and buffy coat [7-101. The erythrocytes were suspended in isotonic buffered saline (90 mM NaCI, 5 mM KCl, 50 mM Na phosphate and 5.6 mM glucose at pH 7.4) after washing and were prepared as follows. (1) erythrocytes with oxygenated hemoglobin; (2) erythrocytes deoxygenated by treating with sodium hydrosulfite; (3) after oxidizing the hemoglobin to methemoglobin with sodium nitrite (20 mM), the erythrocytes were washed and resuspended at pH 5.7 to establish the high-spin ferric state of methemoglobin; (4) erythrocytes treated with potassium cyanide (10 times the total heme) and washed with a buffer at pH 7.4 to obtain the low-spin state of methemoglobin.
183 (a)
(b)
Fig. 1. Flow channels and sedimentation tube, in the inhomogeneous magnetic field. (al For observation of the displacement of an erythrocyte stream line in a iaminar flow [7,8]. The dimension of the channel was 4~0.4~ 150 mm, and the width of the stream line (shown by the dotted line) was ca. 80 pm. (b) For detection of excess flow of erythrocytes to the side branch 191.The inner diameter of the main cylinder was 2.0 mm and that of the side branch 1.0 mm. Cc) Measurement of the erythrocyte sedimentation rate [lo]; the blood suspension was packed in a Westergren tube (inside diameter 2.5 mm). The inhomogeneous magnetic field was generated from an electromagnet and an iron block with one side tapered, to which the channels and the tube were tightly attached. The magnetic flux density around the model channel was measured point by point with a gauss meter, then the spatial gradient and the “averaged” value of the product, B X d B/dz, were calculated [8,9].
Flow channels
An inhomogeneous magnetic field was produced with an electromagnet and a triangular iron block attached to a surface of the magnet. Two flow channels were employed. Figure l(a) shows a rectangular flat cell (4 X 150 X 0.4 mm microslide, Vitro Dynamics, NJ) used to establish a wide laminar buffer flow, containing a narrow stream line (ca. 80 pm) of erythrocyte suspension. The displacement of the stream line due to the paramagnetic attraction was observed by microscopic photography [7,8]. Figure l(b) shows a glass cylinder (outside diameter 4.0 mm, inside diameter 2.0 mm) with a side branch from which a small portion of the erythrocyte flow was taken to detect small changes in the distribution of flowing erythrocytes. The increase of erythrocytes due to the paramagnetic attraction was quantified by the determination of hemoglobin concentration. Figure l(c) shows how erythrocyte sedimentation rate was measured with a Westergren glass tube, placed upright along the iron block [lo]. RESULTS AND DISCUSSION
Displacement of erythrocyte stream line in laminar flow (781
Using the flow channel shown in Fig. l(a), the position of the narrow stream line was measured on microscopic photographs before and during the application of the magnetic field, and the displacement of the stream line due to magnetic attraction was obtained by comparing the two values. Figure 2 shows the displacement of the stream line of erythrocyte suspension, whose diameter is ca. 80 pm in the wide laminar flow (Fig. l(a)). The displacement is detected only for paramagnetic erythrocytes, and not for oxygenated erythrocytes containing diamagnetic
a4
I
ra3
E
(‘I
L!!
!a2
,D
ep
5
0 at
0
10
20 30
40
Mvp =
g
LO
Lo4
5
E0.s ::
0 ff
fd’
/* SL
a4
Bat
0’ 0
5
IO
IS
Harmtwit/%
Fig. 2. Displacement of the etythrocyte stream line as functions of (a) the product of the magnetic flux density and its gradient, (b) the square of the magnetic moment of iron in hemoglobin, which is proportional to the magnetic susceptibility, Cc)flow velocity, and Cd)hematocrit value of the etythrocyte stream. Standard experimental conditions unless specified: flow velocity 0.7 mm/s, average value of B XdB/dz 29 T’/m. For erythrocytes containing high-spin methemoglobin (hematocrit of 6%), containing high-spin methemoglobin (S = 5/2) (m), low-spin methemoglobin (S = l/Z) (01, deoxy-hemoglobin (S = 2) (01, and oxy-hemoglobin (S = 0) (a). Standard deviations are smaller than the symbol size. (For details, see refs. 7 and 8).
oxyhemoglobin. The displacement became larger with the increase of: (1) the product of the magnetic field strength and its spatial gradient; (2) the magnetic susceptibility of hemoglobin in erythrocytes; (3) the reciprocal of the flow velocity; (4) the hematocrit of the suspension. The forces acting on a flowing paramagnetic particle are I;;n_ and F, which are now described. The force F_ is due to attractive magnetic interaction. Neglecting the Lorentz force and the induced Hall effect (because they are small) F,,=,I&L-r(B,xdB,/dz) where x is the paramagnetic susceptibility of the material, V the volume, B, and dB,/dz the magnetic flux density and its gradient in the z coordinate (z is the direction of the magnetic attraction), and ,U is the magnetic permeability. The frictional Stokes force Ff gives resistance for the displacement
185
where u is the velocity of displacement, and R the hydrodynamic radius of the moving particle in a medium of viscosity q. Ff is equilibrated to Fmg within a short time. From these tivo equations, the velocity of displacement u is obtained, and by integrating u along the path (y axis) the estimate of displacement L can be calculated: L = k=u dr = jYzFm,$(6~~~Rv)
dy = V,y/(6mjpRv)
Yl
x jY*Bz(dBz/dr)
dy
Yl
where y, and yz are the y coordinates of the particular erythrocytes at t = 0 and at t = T when the observation was made, respectively, and u is the flow velocity (y direction); thus dt = dy/v. Although the displacement of the erythrocyte stream line occurred in accordance with the above theory, the observed displacement is much larger than the calculated value for a single erythrocyte. Moreover, the displacement depended on the ‘hematocrit of the erythrocyte suspension (Fig. 2(d)). These results show that a group of erythrocytes (in a “volume”) is attracted as a whole by the magnetic force, by this experimental arrangement, as discussed previously [8]. Asymmetric distribution of jlowing erythrocytes in a vessel The attraction of erythrocytes by a strong inhomogeneous magnetic field has been observed [9] with the setup shown in Fig. l(b). A similar flow channel was tested for the separation of paramagnetic (malaria infected) erythrocytes in human blood by Heidelberger et al. in 1946 [ll], but that trial was unsuccessful because the magnetic field strength was too low. In order to separate paramagnetic cells from blood, an extremely high gradient magnetic field is needed [5,6,121. As we have already shown, with paramagnetic erythrocytes containing the high-spin methemoglobin, the proportion of erythrocytes skimmed into the side branch of the flow channel of Fig. 1 (b) is increased by magnetic attraction [9]. The degree of attraction increases linearly with the magnetic susceptibility of erythrocytes, with the product of magnetic field strength and its spatial gradient (but it saturated above ca. 20 T2/m) and with the reciprocal of the flow velocity. Further, a hematocrit dependence was found with maximal attraction at hematocrit readings of ca. 5%, while at 45% no attraction was detected. In the case of mixed suspensions containing erythrocytes with high-spin methemoglobin (paramagnetic) and oxygenated erythrocytes (diamagnetic), the attraction reached a maximum at the “partial hematocrit” for the paramagnetic erythrocytes of ca. 5% and remained nearly constant with further increases of “partial hematocrit” [91. In order to quantify the degree of the magnetic attraction of deoxygenated erythrocytes, we have to measure anaerobically the amount of erythrocytes skimmed into the side branch. Therefore, a spectrophotometer with long optical fiber was attached at the rectangular side branch just below the magnetic field, to take
186
Fig. 3. Excess flow of erythrocytes into the side branch as functions of (a) the product of the magnetic flux density and its gradient, (b) the square of the magnetic moment of iron in hemoglobin, which is proportional to the magnetic susceptibility, (c) flow velocity, and (d) hematocrit value of the erythrocyte suspension. Standard experimental condition unless specified: flow velocity 2.5 mm/s, average value of B xdB/dz 60 T’/m. For erythrocytes (hematocrit of 5%), containing high-spin methemoglobin (S = 5/2) (ml, low-spin methemoglobin (S = l/2) (01, deoxyhemoglobin (S = 2) CO), and oxyhemoglobin (S = 0) (0). The data are shown with standard deviation (bars).
difference spectra before and after exposure to the magnetic field. The changes for the skimmed erythrocytes AV are defined as AV- (amount with field)/(amount without field) - 1. Figure 3 shows the results. AV increased in proportion to the product of the magnetic field strength and its spatial gradient, but saturated at weak magnetic fields (20 T’/m) (Fig. 3(a)). AV also increased in proportion to the magnetic susceptibility of hemoglobin derivatives in the erythrocytes (Fig. 3(b)), and the reciprocal of the flow velocity (Fig. 3(c)). The effect is maximal at an optimal hematocrit of ca. 5% (Fig. 3(d)). Further, Al/ varied with the degree of deoxygenation, in proportion to the estimated magnetic susceptibility. These phenomena can be interpreted as arising from the asymmetric distribution of flowing erythrocytes, made by their paramagnetic interaction with the magnetic field in the cylindrical vessel. The saturation phenomena, at high magnetic field and/or at high hematocrit, may arise from collisions between erythrocytes and collisions with the vessel wall, which form local eddy currents and turbulent flow, and which destroy the magnetic field-induced asymmetry in the distribution. Therefore, as the collision rate increases with increasing the magnetic
187
field and/or the hematocrit, apparently suppressed. Acceleration
of erythrocyte
the magnetic
sedimentation
effect (asymmetric
distribution)
is
rate [lOI
The sedimentation rate of paramagnetic erythrocytes in a Westergren tube increased in a spatially inhomogeneous magnetic field, while no magnetic effect was detected with diamagnetic erythrocytes. This phenomenon is similar to the so-called Boycott effect [13], i.e. the accelerated sedimentation in an inclined cylinder or channel [14]. However, the detailed mechanism of this effect is not fully understood. CONCLUSION
The effect of an external inhomogeneous magnetic field on the flow of erythrocytes containing paramagnetic hemoglobin was studied systematically, with three experimental setups. The results obtained are summarized below. (1) Paramagnetic erythrocytes are attracted by an inhomogeneous magnetic field. (2) The degree of attraction is proportional to (a) the product of magnetic field strength and its spatial gradient, (b) the magnetic susceptibility of hemoglobin, and (c) the reciprocal of the flow velocity. The attraction is detectable with model flow channels in an inhomogeneous magnetic field of above 10 T2/m. (3) The degree of attraction depends on the hematocrit reading, with maximum at ca. 5%. (4) The asymmetric distribution of venous, deoxygenated blood flow in an inhomogeneous magnetic field of above 100 T2/m may induce some biological effect. ACKNOWLEDGMENT
This work was supported in part by grants from the Ministry of Education, Science and Culture of Japan, Nissan Science Foundation, and Ehime Health Foundation. References 1 I.I.H. Chen and S. Saha, J. Bioelectricity, 3 (1984) 293. 2 M. Murayama, Nature, 206 (1965) 420. 3 A.S. Brody, M.P. Sorette, C.A. Gooding, J. Listerud, M.R. Clark, W.C. Mentzer, T.L. James, Invest. Radio]., 20 (1985) 560. 4 A. Yamagishi, T. Takeuchi, T. Higashi and M. Date, Physica B, 177 (1992) 523. 5 D. Melville, F. Paul and S. Roath, Nature, 255 (1975) 706. 6 E.H. Dunlop, W.A. Feiler and M.J. Mattione, Biotech. Advs., 2 (1984) 63. 7 M. Okazaki, N. Maeda and T. Shiga, Experientia, 42 (1986) 842.
R.C. Brasch
and
188 8 9 10 11 12 13 14
M. Okazaki, N. Maeda and T. Shiga, Eur. Biophys. J., 14 (1987) 139. M. Okazaki, K. Kon, N. Maeda and T. Shiga, Physiol. Chem. Phys. Med. NMR, 20 (1988) 3. M. Okazaki, A. Seiyama, K. Kon, N. Maeda and T. Shiga, J. Colloid Interface Sci., 146 (1991) 590. M. Heidelberger, M.M. Meyer and C.R. Damarest, J. Immunol., 52 (1946) 325. J.A. Oberteuffer, IEEE Trans. Magn., 9 (1973) 303. A.E. Boycott, Nature, 104 (1920) 532. K. Abe, Y. Takano and S. Oka, Biorheology, 23 (1986) 17.