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Measurement of magnetic susceptibility and MR contrast agent concentration
Magnetic Resonance Imaging, Vol. 12, No. 6, pp. 859-864, 1994 Copyright 0 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0730-725X/94 $6.00 + .oO
Pergamon
0730-725X(94)EOO27-Y
l Original Contribution
MEASUREMENT OF MAGNETIC SUSCEPTIBILITY AND MR CONTRAST AGENT CONCENTRATION J. WEIS,* S. NILSSON,?A. ERICSSON,~M. WIKSTR~~M,~ G.O. SPERBER,~AND A. HEMMINGSSON~ *Institute of Measurement Science, Slovak Academy of Sciences, Dubravska cesta 9, 842 19 Bratislava, Slovakia tDepartment of Diagnostic Radiology, University Hospital, Uppsala University, S-751 85 Uppsala, Sweden SDepartment of Physiology and Medical Biophysics, Biomedical Centre, Uppsala University, S-751 23 Uppsala, Sweden This paper describes an MR imaging method for determining magnetic susceptibility constants of solutions containing paramagnetic contrast agents. The method’s validity is demonstrated on Gd(DTPA) and Dy(DTPA) water solutions. The method can be used for measurement of the volume magnetic susceptibility or concentration of contrast agents in biological tissues. Keywords: Magnetic susceptibility; Magnetic field measurement; Contrast agents; Myocardial infarction.
modification of Maudsley’s13,14 spectroscopic method described elsewhere. l5 This approach is insensitive to RF excitation imperfections, steady state effects, spatial variations of the received NMR signal, amplitude and phase characteristics of the hardware. It is not necessary to know the spin density distribution though it should be non-zero. These facts are of great advantage compared to other methods.9-‘2 The measurements were performed in a superconductive whole body equipment operating at B, = 0.5 T and (128,128,16) complex data matrix were measured (128 phaseencoding steps, 16 gradient echo sets15). The total measurement time was approximately 14 min (TR = 200 ms, 2 acquisitions). The proton spectrum was reconstructed for each voxel(l.37 x 1.37 x 10 mm3) of the measured slice (FOV = 175 mm, 10 mm slice thickness) by 3D Fourier transform. Figure 1 shows an example of the proton spectrums computed from the voxel row indicated by the white mark on a transverse slice of pig’s heart (Fig. 2A). Whereas static field variation is manifested in shift of the local voxel’s spectra, transverse relaxation as well as average magnetic field inhomogeneity across voxel is seen as line broadening. Magnetic field distribution was computed from the shifts of the highest maximum on the spectral axis (Fig. 1). The position of the maximum relative to the reference frequency was determined from the centre of
INTRODUCTION During the past years many papers have been published describing the influence of different concentrations of paramagnetic and superparamagnetic contrast agents on the signal intensity of hydrogen nuclei. While the general relaxation theory is well established,le3 the specifics of relaxation in biological tissues4s5 and the mechanism of the contrast agents distribution within various organs and pathologies are still debated.6-8 Therefore a method for direct and easy available measurements of the susceptibility constants or concentration of contrast agents by MRI equipment is demanded. In this paper we describe an MR imaging method for determining volume (molar) magnetic susceptibility of a solution (biological tissues) containing paramagnetic contrast agents by measuring its magnetic field perturbation. Experiences from the measurement on phantoms were used for proposal of a simple model, which enables estimation of contrast agent concentration differences between ischemic and nonischemic myocardial tissues of excised pig’s heart.
METHODS Magnetic Field Measurement For measurement of magnetic field perturbation many techniques have been developed.‘-” We used a RECEIVED
7/22/93; ACCEPTED
2/8/94.
Address correspondence 859
to J. Weis.
Magnetic Resonance Imaging 0 Volume 12, Number 6, 1994
860
PPM Fig. I. Proton
spectrum
of the voxel row indicated
by the white mark in Fig. 2A.
Fig. 2. (A) Transverse, (B) sagittal image (TRITE 500/30) of an excised heart of pig. White mark indicated voxel row from which the spectrum (Fig. 1) was taken. (C) Magnetic field distribution of the same transversal slice after correction for background inhomogeneity, (D) mask matrix used for calculation of average magnetic induction of whole slice (grey and white pixels) and at infarcted area (white pixels).
861
Magnetic susceptibility and contrast agent concentration 0 J. WEIS ET AL.
the linewidth at the half height. For this purpose we used the cubic spline interpolation algorithm. Magnetic Susceptibility Measurement The phantom arrangement shown in Fig. 3 was used for magnetic susceptibility measurements. The phantom consisted of a basin (100 x 150 x 200 mm3) containing tap water with plastic probes (+ = 14 mm i.d., approximately 80 mm long). The probes were filled with Gd(DTPA) water solutions (0.125,0.25,0.5, 1.O, 5 .O mM - from the left). The long axes of the probes were parallel to the static magnetic field. Fig. 3A shows a transverse slice of the phantom measured by conven-
tional GRASS technique (TR/TE 13/500 ms). The magnetic field distributions in the phantom with and without probes are shown in Figs. 3B and 3C. Magnetic field variations of the background in Fig. 3C were in the interval (-0.4; 0.1) ppm. This arrangement where the cylindric probes are parallel to the static magnetic field is the most advantageous because of its zero inhomogeneous bulk magnetic susceptibility component.i6 Further, magnetic induction outside of the cylinders is not influenced by the measured paramagnetic solution. Magnetic induction inside the (long) cylinder is definedI as: B; =
1+ ; (
B, 1
where x is the volume magnetic susceptibility of the solution inside the cylinder and B,, the magnetic induction of the static magnetic field. The rationalized SI volume magnetic susceptibility x (in ppm) of the solution can be well estimated using’? n
X=471.CCiXM,,i i=l
(2)
where i is the species index, cj is the concentration of i in mM, and xM,i is the molar susceptibility of species i in cm3/mol. By subtraction of the background magnetic distribution (Fig. 3C) from the magnetic field distribution of the probes (Fig. 3B) we obtained the magnetic induction deviation AB caused by the paramagnetic solution. Combining Eqs. (1) and (2) for the magnetic induction deviation AB yields: AB=
4
yrqM
U-9
(C) Fig, 3. Arrangement of the probes filled by water solution ofGd(DTPA): fromtheleft:0.125,0.25,0.5, 1.0,5.0mM. (A) T,-weighted spin density (TE/TR 13/500 ms). Magnetic field distributions in the water basin with(B) and without (C) probes.
where AB is in ppm, c concentration of paramagnetic agents in mM, and X~ molar susceptibility of paramagnetic agents in cm3/mol. Equation (3) is good approximation because the water concentration in our paramagnetic solution is practically equal to that in distilled water.” Experimental results for Gd(DTPA) and Dy(DTPA) solutions are shown in Fig. 4. Full lines in Fig. 4 are calculated for the theoretical values xM,dGd = 0.026, x~,~,, = 0.047 cm3/mol (T = 298K).16*‘9*20 From the slope of the least squares fitted line of experimental values [O*OGd(DTPA); +++ Dy(DTPA)] we calculated molar magnetic susceptibilities x~, dd = 0.023, xM,DY= 0.049 cm3/mol. We believe that the concurrence between the theoretical and experimental results of molar susceptibilities is good.
8h2
Magnetic Resonance Imaging 0 Volume 12, Number
6
Fig. 4. Magnetic field deviations cies, 0.0 Gd(DTPA), and +++
caused by Gd(DTPA)
Dy(DTPA)
and Dy(DTPA) are measured values.
The above mentioned method is possible to use for measurement of the average volume susceptibility of the biological tissues in vitro and for measurement of contrast agents concentration of the tissues in vitro if the volume susceptibility of the measured tissue is known. The tissue samples have to be homogenized and placed in long tubes parallel to &. If the volume susceptibility of the tissue is unknown, concentration of the contrast agents can be estimated from Eq. (3), where AB will be the magnetic induction difference of the probes filled with the same biological tissues in the presence and in the absence of the paramagnetic contrast agents of the molar susceptibility xhl. The most important problem which in general does not enable extrapolation of above mentioned in vitro method to in vivo is bulk magnetic susceptibility (BMS) effect of the measured object. We believe that in certain restricted circumstances extrapolation of our in vitro experiment to in vivo is possible. For example, for larger homogeneous tissue regions where the magnetic field shift caused by BMS effect is reasonably constant. Such areas may exist in brain, liver, muscles, etc. Then the voxels of this region can be approximated by long parallel cylinders as depicted in Fig. 5. The magnetic induction B inside each “cylindric voxel” is given by: (4)
7
water
6, 1994
8
9
10
solutions. Full lines are theoretical dependen-
where x is volume magnetic susceptibility of the tissue inside “cylindric voxel” and BBMs is BMS induced magnetic field shift, which according to our assumption is constant for the whole selected tissue region. Differences in magnetic fields among these “cylindric voxels” are caused only by differences in volume magnetic susceptibility. If changes are caused by paramag-
Z//B0 Fig. 5. Model of the “cylindric voxels” used for estimation of contrast agents concentration differences.
Magnetic susceptibility and contrast agent concentration 0 3. WEISET AL.
netic contrast agents, then according to Eq. (3) it is possible to estimate difference in contrast agent concentration among “cylindric voxels.” Biological Subject We used the model of “cylindric voxels” to estimate the average contrast agent concentration difference between ischemic and non-ischemic tissues of a pig’s heart (Fig. 2). Myocardial infarction was induced in a domestic pig by placing a patched ligature around a diagonal branch of the left anterior descending artery. The appearance of cyanosis distal to the ligature was used as a criterion of successful occlusion. Eighty minutes of occlusion was followed by 40 min of reperfusion before sacrifice. Cd-DTPA-BMA (0.2 mmol/kg b.w.) was injected IV 5 min before sacrifice. Following sacrifice, the heart was extirpated and rinsed in isotonic saline to remove remaining blood. The heart was examined ex vivo at room temperature in the MR equipment and then cut into thin slices and soaked for about 20 min in a 1% aqueous solution of triphenyltetrazolium chloride (TTC) at 37°C. The slices were then inspected for unstained areas corresponding to infarction. Normal myocardium stained brick-red. The heart was investigated with sagittal and transverse multi-slice spin echo images with TRITE of 500/30 (Figs. 2A and 2B), 1500/30,70 and 1500/30,120 using a saddle-shaped coil with a diameter of 13 cm. The proton magnetic resonance spectroscopic measurement was performed for the same transverse slice as in Fig. 2A. Figure 1 shows proton spectra of the voxel row across the infarcted area (white mark in the Fig. 2A). Spectral lines from the infarcted area (60 < X < 70) are significantly broader and shifted towards positive ppm values. This is presumably caused by higher concentration of Gd(DTPA) in infarcted myocardium. Magnetic field distribution of the measured transversal slice Fig. 2C, was computed from the shift of the spectral lines (Fig. 1) and corrected for background inhomogeneities caused by the electromagnet’s coil system. Magnetic field background was measured in a separate experiment. A large plastic cylinder (+ = 95 mm i.d., 250 mm long) filled by tap water was used for this purpose. Magnetic field shifts of the pig’s heart were calculated only from the voxels where the amplitude of the spectral line was higher than l/4 of the highest spectral line, that is, only from good pronounced spectral lines. As seen from Fig. 2C, the magnetic field induction is not constant throughout the measured slice. Besides expected higher magnetic field due to higher contrast agents concentration in the infarcted region, there are also other magnetic field fluctuations. The strongest on the left side is probably caused by inhomogeneous tissue region due to a large blood vessel run-
863
ning perpendicular to the direction of B,. Further fluctuations can be caused by the local inhomogeneous BMS shift contributions. For elimination of the parasite magnetic field fluctuations we computed average magnetic induction from all pixels of the measured area (Fig. 2D grey and white pixels) and average magnetic induction from infarcted region (white pixels). From the difference AB between these average magnetic inductions we estimated the difference of average contrast agents concentration by using Eq. (3), where X~ = XGd.This difference was 0.14 mM. It was not possible for us to check this value by another independent method or by in vitro measurement. Together with the heart we measured the magnetic field deviation inside the probes with reference concentration of Gd-DTPA. These probes can be seen in Figs. 2A-C. The left probe (Figs. 2A and 2C) was filled with water solution containing 0.125 mM and right probe contained 5 mM of Gd-DTPA. From the difference of average magnetic induction inside the probes we calculated concentration difference. This result was about 12% higher. The error could be caused mainly by BMS shift induced by the paramagnetic heart. An example of this effect can be seen at reference probe 0.125 mM Gd-DTPA-BMA in Fig. 2C. The magnetic field is higher in the voxels closer to the heart. DISCUSSION TTC-staining shows infarction as pale areas with small hemorrhages. Corresponding to unstained areas there was a strong contrast enhancement in the reperfused infarcted area seen in T, -weighted (Figs. 2A and 2B) TRITE of 500130, transverse and sagittal images. In T,-weighted TRITE of 1500/70, images there was a signal increase in infarcted areas compared to nonischemic myocardium. Irreversibly injured reperfused myocardium is characterized by cellular swelling because of edema, accelerated structural disintegration of the myocytes, accentuated interstitial edema due to increased capillary permeability and intramyocardial hemorrhage. Edema formation and hemorrhage depended on the severity and duration of ischemia and reflow. Administration of Gd-DTPA-BMA after reperfusion will result in a homogeneous (both intra- and extracellular) contrast accumulation in the reperfused, infarcted myocardium with a delayed washout of contrast medium because of compression of small vessels secondary to the edema. The second mechanism of increasing Gd-DTPA-BMA concentration difference between infarcted and normal tissues is the rapid decrease of the contrast medium in plasma and normal tissue by renal excretion with a blood (blood-concentration half life of Gd-DTPA-BMA was reported to be 70
864
Magnetic Resonance Imaging 0 Volume 12, Number 6, 1994
mini8). The average concentration difference of GdDTPA-BMA between infarcted and normal tissues was 0.14 mM, according to the method above described. This is seen best in Tt-weighted sequences (Figs. 2A and 2B) where Gd-DTPA-BMA shortens T, , resulting in a prominent enhancement. Edema formation prolongs T2, with high signal intensity in T,-weighted sequences. The T2 effect of Gd-DTPA-BMA is small with this concentration and will not influence the T, value. CONCLUSION We have described a method which may be easily implemented on MRI equipment for measuring volume magnetic susceptibility of biological tissues. We have indicated the potential of this method in the estimation of differences in susceptibility or contrast agents concentrations in biological tissues. Acknowledgments-Financial support by the Swedish Medical Research Council, project No. 00-6676 and by Slovak Academy of Sciences, project No. 999266/92, 2/999266/92 are gratefully acknowledged.
REFERENCES 1. Solomon, I. Relaxation processes in a system of two spins. Phys. Rev. 99:559-565; 1955. 2. Bloembergen, N. Proton relaxation times in paramagnetic solutions. J. Chem. Phys. 27:572-581; 1957. 3. Gadian, D.G.; Payne, J.A.; Bryant, D.J.; Young, I.R.; Carr, D.H.; Bydder, G.M. Gadolinium-DTPA as acontrast agent in MR imaging-Theoretical projections and practical observations. J. Comput. Assist. Tomogr. 9: 242-251; 1985. 4. Fisel, C.R.; Ackerman, J.L.; Buxton, R.B.; Garrido, L.; Belliveau, J.W.; Rosen, B.R.; Brady, T.J. MR contrast due to microscopically heterogeneous magnetic susceptibility: Numerical simulations and applications to cerebral physiology. Magn. Reson. Med. 17:336-347; 1991. 5. Hardy, P.A.; Henkelman, R.M. Transverse relaxation rate enhancement caused by magnetic particulates. Magn. Reson. Imaging 7~265-275; 1989. A.J.; Cirton, M.E.; Inscoe, S.W.; 6. Choyke,P.L.;Frank, Carvlin, M.J.; Black, J.L.; Austin, H.A.; Dwyer, A.J.; Dynamic Gd-DTPA-enhanced MR imaging of the kidney: Experimental results. Radiology 170:713-720; 1989.
7. Li King, C.P.; Quisling, R.G.; Armitage, F.E.; Richardson, D.; Mladinich, C.H.; In vivo evaluation of GdDTPA conjugated to dextran in normal rabbits. Magn. Reson. Imaging 10:439-444; 1992. 8. Wikstrom, M.; Martinussen, H.J.; Wikstrom, G.; Ericsson, A.; Nyman, R.; Waldenstrom, A. Hemmingsson, A. MR imaging of acute myocardial infarction in pigs using Gd-DTPA-labeled dextran. Acta Radiol. 33:301308; 1992. 9. Sekihara, K.; Matsui, S.; Kohno, H. NMR imaging for magnets with large nonuniformities. IEEE Trans. Med. Imag. MI-4:193-199; 1985. 10. Willcott, M.R.; Mee, G.L.; Chesick, J.P. Magnetic field mapping in NMR imaging. Magn. Reson. Imaging 5: 301-306; 1987. II. Young, I.R.; Khenia, D.G.T.; Davis, C.H.; Gadian, D.G.; Cox, I.J.; Ross, B.D.; Byder, G.M. Clinicalmagnetic susceptibility mapping of the brain. J. Comput. Assist. Tomogr. 11(1):2-6; 1987. 12. Glover G.H.; Schneider, E. Three-point Dixon technique for true water/fat decomposition with Be inhomogeneity correction. Mugn. Reson. Med. 18:371-383; 1991. 13. Maudsley, A.A.; Oppelt, A.; Ganssen, A. Rapid measurement of magnetic field distribution using nuclear magnetic resonance. Siemens Forschung und Entwicklung Ber. Bd. 8:326-329; 1979. 14. Maudsley A.A.; Simon, H.E.; Hilal, S.K. Magnetic field measurement by NMR imaging. J. Phys. E: Sci. Instrum. 17:216-220; 1984. 15. Weis, J.; Frollo, I.; Budinsky, L. Magnetic field distribution measurement by the modified FLASH method. Zeitschriftf. Naturforsch. 44a:1151-1154; 1989. 16. Chu, Simon C.-K.; Xu, Y.; Balschi, J.A.; Springer, C.S. Jr. Bulk magnetic susceptibility shifts in NMR studies of compartmentalized samples: Use of paramagnetic reagents. Mugn. Reson. Med. 13:239-262; 1990. 17. Weast, R.C. (Ed). Handbook of Chemistry and Physics 64th ed. Boca Raton, Fl: CRC Press; 1984: p. D-257. 18. VanWagoner, M.; O’Toole, M.; Worah, D.; Leese, P.T.; Quay, S.S. A Phase I clinical trial with gadodiamid injection, a nonionic MRI enhancement agent. Invest. Radial. 26( 1):980-986, 1991. 19. Josephson, L.; Bigler, J.; White, D. The magnetic properties of some materials affecting MR images. Magn. Reson. Med. 22:204-208; 1991. 20. Myers, R. J. Nuclear Magnetism and Magnetic Resonance Spectroscopy. Englewood Cliffs, NJ: Prentice Hall; 1973: p. 65.
Pergamon
0730-725X(94)EOO27-Y
l Original Contribution
MEASUREMENT OF MAGNETIC SUSCEPTIBILITY AND MR CONTRAST AGENT CONCENTRATION J. WEIS,* S. NILSSON,?A. ERICSSON,~M. WIKSTR~~M,~ G.O. SPERBER,~AND A. HEMMINGSSON~ *Institute of Measurement Science, Slovak Academy of Sciences, Dubravska cesta 9, 842 19 Bratislava, Slovakia tDepartment of Diagnostic Radiology, University Hospital, Uppsala University, S-751 85 Uppsala, Sweden SDepartment of Physiology and Medical Biophysics, Biomedical Centre, Uppsala University, S-751 23 Uppsala, Sweden This paper describes an MR imaging method for determining magnetic susceptibility constants of solutions containing paramagnetic contrast agents. The method’s validity is demonstrated on Gd(DTPA) and Dy(DTPA) water solutions. The method can be used for measurement of the volume magnetic susceptibility or concentration of contrast agents in biological tissues. Keywords: Magnetic susceptibility; Magnetic field measurement; Contrast agents; Myocardial infarction.
modification of Maudsley’s13,14 spectroscopic method described elsewhere. l5 This approach is insensitive to RF excitation imperfections, steady state effects, spatial variations of the received NMR signal, amplitude and phase characteristics of the hardware. It is not necessary to know the spin density distribution though it should be non-zero. These facts are of great advantage compared to other methods.9-‘2 The measurements were performed in a superconductive whole body equipment operating at B, = 0.5 T and (128,128,16) complex data matrix were measured (128 phaseencoding steps, 16 gradient echo sets15). The total measurement time was approximately 14 min (TR = 200 ms, 2 acquisitions). The proton spectrum was reconstructed for each voxel(l.37 x 1.37 x 10 mm3) of the measured slice (FOV = 175 mm, 10 mm slice thickness) by 3D Fourier transform. Figure 1 shows an example of the proton spectrums computed from the voxel row indicated by the white mark on a transverse slice of pig’s heart (Fig. 2A). Whereas static field variation is manifested in shift of the local voxel’s spectra, transverse relaxation as well as average magnetic field inhomogeneity across voxel is seen as line broadening. Magnetic field distribution was computed from the shifts of the highest maximum on the spectral axis (Fig. 1). The position of the maximum relative to the reference frequency was determined from the centre of
INTRODUCTION During the past years many papers have been published describing the influence of different concentrations of paramagnetic and superparamagnetic contrast agents on the signal intensity of hydrogen nuclei. While the general relaxation theory is well established,le3 the specifics of relaxation in biological tissues4s5 and the mechanism of the contrast agents distribution within various organs and pathologies are still debated.6-8 Therefore a method for direct and easy available measurements of the susceptibility constants or concentration of contrast agents by MRI equipment is demanded. In this paper we describe an MR imaging method for determining volume (molar) magnetic susceptibility of a solution (biological tissues) containing paramagnetic contrast agents by measuring its magnetic field perturbation. Experiences from the measurement on phantoms were used for proposal of a simple model, which enables estimation of contrast agent concentration differences between ischemic and nonischemic myocardial tissues of excised pig’s heart.
METHODS Magnetic Field Measurement For measurement of magnetic field perturbation many techniques have been developed.‘-” We used a RECEIVED
7/22/93; ACCEPTED
2/8/94.
Address correspondence 859
to J. Weis.
Magnetic Resonance Imaging 0 Volume 12, Number 6, 1994
860
PPM Fig. I. Proton
spectrum
of the voxel row indicated
by the white mark in Fig. 2A.
Fig. 2. (A) Transverse, (B) sagittal image (TRITE 500/30) of an excised heart of pig. White mark indicated voxel row from which the spectrum (Fig. 1) was taken. (C) Magnetic field distribution of the same transversal slice after correction for background inhomogeneity, (D) mask matrix used for calculation of average magnetic induction of whole slice (grey and white pixels) and at infarcted area (white pixels).
861
Magnetic susceptibility and contrast agent concentration 0 J. WEIS ET AL.
the linewidth at the half height. For this purpose we used the cubic spline interpolation algorithm. Magnetic Susceptibility Measurement The phantom arrangement shown in Fig. 3 was used for magnetic susceptibility measurements. The phantom consisted of a basin (100 x 150 x 200 mm3) containing tap water with plastic probes (+ = 14 mm i.d., approximately 80 mm long). The probes were filled with Gd(DTPA) water solutions (0.125,0.25,0.5, 1.O, 5 .O mM - from the left). The long axes of the probes were parallel to the static magnetic field. Fig. 3A shows a transverse slice of the phantom measured by conven-
tional GRASS technique (TR/TE 13/500 ms). The magnetic field distributions in the phantom with and without probes are shown in Figs. 3B and 3C. Magnetic field variations of the background in Fig. 3C were in the interval (-0.4; 0.1) ppm. This arrangement where the cylindric probes are parallel to the static magnetic field is the most advantageous because of its zero inhomogeneous bulk magnetic susceptibility component.i6 Further, magnetic induction outside of the cylinders is not influenced by the measured paramagnetic solution. Magnetic induction inside the (long) cylinder is definedI as: B; =
1+ ; (
B, 1
where x is the volume magnetic susceptibility of the solution inside the cylinder and B,, the magnetic induction of the static magnetic field. The rationalized SI volume magnetic susceptibility x (in ppm) of the solution can be well estimated using’? n
X=471.CCiXM,,i i=l
(2)
where i is the species index, cj is the concentration of i in mM, and xM,i is the molar susceptibility of species i in cm3/mol. By subtraction of the background magnetic distribution (Fig. 3C) from the magnetic field distribution of the probes (Fig. 3B) we obtained the magnetic induction deviation AB caused by the paramagnetic solution. Combining Eqs. (1) and (2) for the magnetic induction deviation AB yields: AB=
4
yrqM
U-9
(C) Fig, 3. Arrangement of the probes filled by water solution ofGd(DTPA): fromtheleft:0.125,0.25,0.5, 1.0,5.0mM. (A) T,-weighted spin density (TE/TR 13/500 ms). Magnetic field distributions in the water basin with(B) and without (C) probes.
where AB is in ppm, c concentration of paramagnetic agents in mM, and X~ molar susceptibility of paramagnetic agents in cm3/mol. Equation (3) is good approximation because the water concentration in our paramagnetic solution is practically equal to that in distilled water.” Experimental results for Gd(DTPA) and Dy(DTPA) solutions are shown in Fig. 4. Full lines in Fig. 4 are calculated for the theoretical values xM,dGd = 0.026, x~,~,, = 0.047 cm3/mol (T = 298K).16*‘9*20 From the slope of the least squares fitted line of experimental values [O*OGd(DTPA); +++ Dy(DTPA)] we calculated molar magnetic susceptibilities x~, dd = 0.023, xM,DY= 0.049 cm3/mol. We believe that the concurrence between the theoretical and experimental results of molar susceptibilities is good.
8h2
Magnetic Resonance Imaging 0 Volume 12, Number
6
Fig. 4. Magnetic field deviations cies, 0.0 Gd(DTPA), and +++
caused by Gd(DTPA)
Dy(DTPA)
and Dy(DTPA) are measured values.
The above mentioned method is possible to use for measurement of the average volume susceptibility of the biological tissues in vitro and for measurement of contrast agents concentration of the tissues in vitro if the volume susceptibility of the measured tissue is known. The tissue samples have to be homogenized and placed in long tubes parallel to &. If the volume susceptibility of the tissue is unknown, concentration of the contrast agents can be estimated from Eq. (3), where AB will be the magnetic induction difference of the probes filled with the same biological tissues in the presence and in the absence of the paramagnetic contrast agents of the molar susceptibility xhl. The most important problem which in general does not enable extrapolation of above mentioned in vitro method to in vivo is bulk magnetic susceptibility (BMS) effect of the measured object. We believe that in certain restricted circumstances extrapolation of our in vitro experiment to in vivo is possible. For example, for larger homogeneous tissue regions where the magnetic field shift caused by BMS effect is reasonably constant. Such areas may exist in brain, liver, muscles, etc. Then the voxels of this region can be approximated by long parallel cylinders as depicted in Fig. 5. The magnetic induction B inside each “cylindric voxel” is given by: (4)
7
water
6, 1994
8
9
10
solutions. Full lines are theoretical dependen-
where x is volume magnetic susceptibility of the tissue inside “cylindric voxel” and BBMs is BMS induced magnetic field shift, which according to our assumption is constant for the whole selected tissue region. Differences in magnetic fields among these “cylindric voxels” are caused only by differences in volume magnetic susceptibility. If changes are caused by paramag-
Z//B0 Fig. 5. Model of the “cylindric voxels” used for estimation of contrast agents concentration differences.
Magnetic susceptibility and contrast agent concentration 0 3. WEISET AL.
netic contrast agents, then according to Eq. (3) it is possible to estimate difference in contrast agent concentration among “cylindric voxels.” Biological Subject We used the model of “cylindric voxels” to estimate the average contrast agent concentration difference between ischemic and non-ischemic tissues of a pig’s heart (Fig. 2). Myocardial infarction was induced in a domestic pig by placing a patched ligature around a diagonal branch of the left anterior descending artery. The appearance of cyanosis distal to the ligature was used as a criterion of successful occlusion. Eighty minutes of occlusion was followed by 40 min of reperfusion before sacrifice. Cd-DTPA-BMA (0.2 mmol/kg b.w.) was injected IV 5 min before sacrifice. Following sacrifice, the heart was extirpated and rinsed in isotonic saline to remove remaining blood. The heart was examined ex vivo at room temperature in the MR equipment and then cut into thin slices and soaked for about 20 min in a 1% aqueous solution of triphenyltetrazolium chloride (TTC) at 37°C. The slices were then inspected for unstained areas corresponding to infarction. Normal myocardium stained brick-red. The heart was investigated with sagittal and transverse multi-slice spin echo images with TRITE of 500/30 (Figs. 2A and 2B), 1500/30,70 and 1500/30,120 using a saddle-shaped coil with a diameter of 13 cm. The proton magnetic resonance spectroscopic measurement was performed for the same transverse slice as in Fig. 2A. Figure 1 shows proton spectra of the voxel row across the infarcted area (white mark in the Fig. 2A). Spectral lines from the infarcted area (60 < X < 70) are significantly broader and shifted towards positive ppm values. This is presumably caused by higher concentration of Gd(DTPA) in infarcted myocardium. Magnetic field distribution of the measured transversal slice Fig. 2C, was computed from the shift of the spectral lines (Fig. 1) and corrected for background inhomogeneities caused by the electromagnet’s coil system. Magnetic field background was measured in a separate experiment. A large plastic cylinder (+ = 95 mm i.d., 250 mm long) filled by tap water was used for this purpose. Magnetic field shifts of the pig’s heart were calculated only from the voxels where the amplitude of the spectral line was higher than l/4 of the highest spectral line, that is, only from good pronounced spectral lines. As seen from Fig. 2C, the magnetic field induction is not constant throughout the measured slice. Besides expected higher magnetic field due to higher contrast agents concentration in the infarcted region, there are also other magnetic field fluctuations. The strongest on the left side is probably caused by inhomogeneous tissue region due to a large blood vessel run-
863
ning perpendicular to the direction of B,. Further fluctuations can be caused by the local inhomogeneous BMS shift contributions. For elimination of the parasite magnetic field fluctuations we computed average magnetic induction from all pixels of the measured area (Fig. 2D grey and white pixels) and average magnetic induction from infarcted region (white pixels). From the difference AB between these average magnetic inductions we estimated the difference of average contrast agents concentration by using Eq. (3), where X~ = XGd.This difference was 0.14 mM. It was not possible for us to check this value by another independent method or by in vitro measurement. Together with the heart we measured the magnetic field deviation inside the probes with reference concentration of Gd-DTPA. These probes can be seen in Figs. 2A-C. The left probe (Figs. 2A and 2C) was filled with water solution containing 0.125 mM and right probe contained 5 mM of Gd-DTPA. From the difference of average magnetic induction inside the probes we calculated concentration difference. This result was about 12% higher. The error could be caused mainly by BMS shift induced by the paramagnetic heart. An example of this effect can be seen at reference probe 0.125 mM Gd-DTPA-BMA in Fig. 2C. The magnetic field is higher in the voxels closer to the heart. DISCUSSION TTC-staining shows infarction as pale areas with small hemorrhages. Corresponding to unstained areas there was a strong contrast enhancement in the reperfused infarcted area seen in T, -weighted (Figs. 2A and 2B) TRITE of 500130, transverse and sagittal images. In T,-weighted TRITE of 1500/70, images there was a signal increase in infarcted areas compared to nonischemic myocardium. Irreversibly injured reperfused myocardium is characterized by cellular swelling because of edema, accelerated structural disintegration of the myocytes, accentuated interstitial edema due to increased capillary permeability and intramyocardial hemorrhage. Edema formation and hemorrhage depended on the severity and duration of ischemia and reflow. Administration of Gd-DTPA-BMA after reperfusion will result in a homogeneous (both intra- and extracellular) contrast accumulation in the reperfused, infarcted myocardium with a delayed washout of contrast medium because of compression of small vessels secondary to the edema. The second mechanism of increasing Gd-DTPA-BMA concentration difference between infarcted and normal tissues is the rapid decrease of the contrast medium in plasma and normal tissue by renal excretion with a blood (blood-concentration half life of Gd-DTPA-BMA was reported to be 70
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Magnetic Resonance Imaging 0 Volume 12, Number 6, 1994
mini8). The average concentration difference of GdDTPA-BMA between infarcted and normal tissues was 0.14 mM, according to the method above described. This is seen best in Tt-weighted sequences (Figs. 2A and 2B) where Gd-DTPA-BMA shortens T, , resulting in a prominent enhancement. Edema formation prolongs T2, with high signal intensity in T,-weighted sequences. The T2 effect of Gd-DTPA-BMA is small with this concentration and will not influence the T, value. CONCLUSION We have described a method which may be easily implemented on MRI equipment for measuring volume magnetic susceptibility of biological tissues. We have indicated the potential of this method in the estimation of differences in susceptibility or contrast agents concentrations in biological tissues. Acknowledgments-Financial support by the Swedish Medical Research Council, project No. 00-6676 and by Slovak Academy of Sciences, project No. 999266/92, 2/999266/92 are gratefully acknowledged.
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