- Email: [email protected]
Three-dimensional NMR microscopy: Improving SNR with temperature and microcoils
Magnetic Resonance inwging, Vol. IO, pp. 279-288, Printed in the USA. All rights reserved.
1992 Copyright 0
0730-725x/92 $5.03 + .oo 1992 Pergamon Press Ltd.
0 Original Contribution THREE-DIMENSIONAL NMR MICROSCOPY: IMPROVING SNR WITH TEMPERATURE AND MICROCOILS E.W.
MCFARLAND
AND
A.
MORTARA
of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA, and Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA, USA
Department
It is widely held that the spatial resolution achievable by NMR microscopic imaging is limited in biological systems by diffusion to approximately l-5 Cm. However, these estimates were developed for specific imaging techniques and represent practical rather than fundamental limits. NMR imaging is limited by the signal-to-noise ratio (SNR). Diffusion effects on spatial resolution can be made arbitrarily small in principle by increasing the gradient strength. The exponential signal attenuation from random spin motion in a gradient, however, will reduce the signal far below the noise level when the voxel size is reduced much below 5pm. Two factors can be optimized to improve the SNR: (1) the inductive linkage between microscopic samples and the detection apparatus and (2) the temperature of the rf probe. In this work, the filling factor was optimized using inductors with diameters less than 1 mm. It is furthermore shown that probe circuit cooling results in significant improvements in SNR, whereas cooling of the preamplifier is of little value when proper noise matching between the resonant circuit and preamplifier is accomplished. Using three-dimensional Fourier imaging techniques, we have obtained images of singlecell organisms with spatial resolution of approximately 6 pm. Practical limitations include mechanical stability of the apparatus, thermal shielding between the sample and probe, and the magnetic susceptibility of the sample. Keywords:
NMR microscopy;
INTRODUCTION
AND
Signal-to-noise
ratio; Cryogenics;
In practice, the magnetic component of a large number of coherent photons is detected by induction. For this method of detection, the SNR has been calculated by many investigators.“-” In NMR microscopy of small samples (d < 1 mm diameter), there is negligible loading of a room temperature coil by the sample, and the original SNR analysis of Hoult and Richards is applicable. I8 The signal detected in a coil surrounding a sample of dimension d, consisting of (r~)~ volume elements, each of dimension Ar, is well understood. Though several general forms might be used for the induced voltage SNR obtained from the nuclear induction, we will use the expression:
THEORY
Since the advent of NMR imaging, there have been ongoing efforts to improve the spatial resolution to the subcellular level.‘-‘5 It is the reduction in SNR from the reduced voxel size that fundamentally limits spatial resolution. At present, the practical limit is approximately 5-10 hrn. The effects of diffusion and bulk motion of nuclei on the NMR signal are well known and are an inconvenience; however, they do not create a fundamental limit to the spatial resolution.r5,i6 We are interested in microscopy of singlecell preparations where coherent motion and regional magnetic susceptibility differences can be neglected. In this regime, several of the rf detection assumptions of medical NMR imaging are no longer valid. In particular, for microsamples the dominant source of noise is no longer a priori the object. In this communication, methods to improve the SNR in practical microscopic applications are described, together with examples from living systems. RECEIVED 7/2/9l; ACCEPTED lO/ 14191. Address correspondence to E.W. McFarland,
Preamplifier.
SNR - (Ar)3py3H;(bw)-1’2
7 i
1
Xf(Tp, T,,R,,R,,F)W(D)~total
time
(1)
where p is the nuclear spin density; y is the nuclear gyromagnetic ratio, Ho is the main field strength, bw is of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106. email: [email protected].
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the bandwidth, and (HI/i) is the magnetic field produced in the volume per unit coil current. f(T,, T,, R,, R,,F) is a function of the probe and sample temperatures TP and T,, their effective resistances, R, and R,, and the amplifier noise figure F. This factor will be discussed in detail below. The factor W(D) is introduced here to represent the reduction in signal intensity due to spin diffusion.” Reducing the resolution element obtainable with a clinical MRI system (Ar approximately 1 mm) to Ar = 1 pm results in a reduction in SNR of approximately 109, simply due to the reduction in the number of spins in the voxel generating the signal. The challenge for the NMR microscopist is to recover as much of that IO9 SNR deficit as possible. The system to be imaged will determine the first several terms in Eq. (1). Assuming we are interested in imaging the ubiquitous H’ nucleus in a small liquid system, a high field strength will be chosen. 10-T magnets are readily available, and the SNR deficit can be reduced in these fields by a factor of 10P2, compared with 1-T clinical MRI systems. The reduction in relaxation contrast at higher fields will be ignored for this comparison. The image bandwidth, bw, involves several factors, and because of considerations of data acquisition time, gradient strength, and field homogeneity, typical values are between 3 and 10 kHz for both MRI and NMR microscopy. The optimal bw has been given by Callaghan and Eccles for an image matrix of size n as r~/aT~.‘~ The bandwidth is predicted to remain constant for any resolution as long as the matrix size remains constant. In fact, for microscopy, diffusion will dominate the signal loss and the broadening of the linewidth from a single volume element. In a spin system of diffusion coefficient D, the minimum gradient strength G is related to the required resolution Ar by: I6 Ar=83
JNlnPl)* 3yG
*
This expression can be solved for the required gradient. The image bandwidth for an object of total dimension d = nAr is then: bw=ynArG=,,ar[DF(:)l]
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terms in Eq. (1). These are essentially the only experimentally variable factors. Filling Factor Improvement The term HI/i reflects the magnetic flux coupling between the NMR photons and the rf receiving coil. I8 The term HI/i is typically maximized by reducing the radius of the coil to approximately that of the sample, thus optimizing the filling factor.” The ideal coil diameter will be approximately that of the sample, d = nAr, where n is the size of the image array. For our studies, cells are contained in micropipettes with diameters of approximately 100-1000 pm (Fig. 1). In the most favorable case, the improvement in HI/i compared with the MRI system will be the inverse of their respective voxel sizes when identical array sizes are used. The lo9 SNR deficit is readily reduced by lo-’ and lop3 on the basis of the field strength and small sample probe geometry, respectively. The remaining factor of 104, however, is an enormous deficit in SNR, and further work is necessary to improve the system for useful microscopic imaging. RF Detector Cooling The other variable under the control of the NMR microscopist is the termf(T,, T,, R,, R,, F) in Eq. (1). As is well known, the noise in NMR is due to thermal noise from the sample and probe circuits.“-I9 The term f ( TP, T,, R,, R,, F) contains the dependence of the SNR on the sample and probe absolute temperatures and their effective resistances. Additionally, the Curie law dependence of the signal on temperature is included. The thermal noise of a given resistance varies as (RT) 1’2. Noise is reduced if resistance and/or temperature are reduced. Unfortunately, liquid biological samples studied in vivo are limited to temperatures T, > 273 K. It is possible to cool the sample and probe circuit to different temperatures, T, and T,. In this case, the model of the probe circuit noise as a series combination of two independent noise generators may be used. One source is due to the actual probe resistance with a noise power of R,T,, and the other is due to the effective series resistance of the sample, R,, with a noise power of R,T,. An estimate of the improvement in SNR that can be achieved by lowering the temperature of the sample and/or coil is given by
.
1
SNR 4 T:(R,T, For our work, we observed the H’ nucleus at the highest field available to us (8.4-T). Efforts were focused on maximizing the H, /i and f (T,, T,, RP, R,, F)
+ R,K)
(2)
where the TsP’ Curie law dependency is included together with the resistive noise power.22 Experimen-
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Fig. 1. Schematic of single-cell probe. The coil circuit is cooled with nitrogen gas at T, (150-300 K). The sample temperature is maintained at T, = 283 K by a separate, warmer, gas stream in gap between the cooled conductors and the sample holder.
tally, R, can be determined by measurement of the circuit Q with the sample in place [ QL = wL/( R, + R,)] and after removing the sample, (Qu = wL/R,). The change in the coil inductance, L, with loading is negligible for small samples. The ratios of the factor f(T,, T,, R,, R,, F) for different temperature conditions can be written using the expressions for the experimentally determined Q’s in Eq.(2) to compare two probe configurations.‘4
_fr
SNRI SNRz
-fi
can be both from a direct reduction in thermal energy and by a reduction in circuit resistance. Above superconducting temperatures, the ohmic resistance of the inductor is well known. For a solid copper wire coil, R, depends on the coil radius r, the wire diameter a, the resistivity p, the number of turns N, and the skin depth 6,. For temperatures above the critical temperature, the decrease in skin depth with decreased rebalances the direct sistivity [6, - (p)‘j2] partially reduction in resistivity with temperature and
R,=p(T)s -m-v++cu(T-273K). s
(3) For microscopy using microcoils (r < 1 mm), QJQL is approximately 1, whereas for large medical MRI systems operating at 1 T, QU/QL is between 5 and 10. The ratio of the coil-to-sample temperature is therefore much more important in the microscopy system. Equation (3) indicates that an SNR increase is obtained by cooling the resonant circuit itself relative to the sample when the coil loading is weak. The increase
For copper, Q! = 0.004 K-l, and the overall effect on Eq. (3) from the ratio of resistances is weak. As materials research progresses and high-critical-temperature materials become available, the resistance dependence of Eq. (3) can be more fully exploited. However, at present the thermal shielding requirements required for superconducting detectors will limit the gains in noise reduction by lost filling factor. The direct noise power reduction will largely determine the benefit in nonsuperconducting coils.
Preamplifier cooling effects. The preamphfier noise figure F is typicaIIy deiined in terms of noise power ratios at the input and output of the device. The depen-
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dency of the NMR signal voltage SNR on preamplifier noise figure is approximately F-l”. The temperature dependence of the ratio of the noise figures for a preamplifier at two different temperatures (F,/F, ) is less explicit for preamplifiers designed using low-noise field effect transistors (FETs). It has been reported by Styles that improvements in SNR can be achieved by cooling the preamplifier as well as the probe circuit.22*23 To compare the cooled and uncooled preamplifiers, the ratio of the noise figures can be expressed in terms of equivalent noise temperatures as
F(C)
-
=
F(T,)
Ts
+
Tn2
Ts
+
Tn,
(4)
where T, is the signal source the noise temperature of the ture T, . In the most general fier noise temperature takes
temperature, and T,, is preamplifier at temperasituation, the FET amplithe form:24
where w
V
=24kT 3 G,
is the noise power spectral density of the amplifiergenerated noise, G, is the transconductance of the FET, T is the FET temperature, R, is the actual source resistance, and R,, is the optimal source resistance obtained by setting: s_ 6’R, -
and solving
0
for R, = R,,
(6) where fi = G,/2aC, is the gain-bandwidth product of the FET and C, its gate capacitance. This value represents the optimal source resistance that the FET gate must see in order to achieve minimum noise figure. If properly matched noisewise, the preamplifier will have a minimum noise temperature:25
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l/2
0 0 -
3
5
I
T
for
fcfr
.
(7)
Equation (7) shows that the noise temperature is only a small fraction of the amplifier’s temperature T if the operating frequency f is low compared with the transistor gain-bandwidth product ft. Additionally, cooling the preamplifier will yield only a marginal noise figure improvement unless the source resistance is very different from the desired R,,. For example, for an fi of 3 GHz and an operating frequency of 300 MHz, cooling the preamplifier from 293 to 163 K under noise-matched conditions yields a decrease in noise temperature of less than 11 K. If a transistor designed for higher frequency is used, say with f, = 30 GHz, this improvement is reduced to less than 1.1 K! These considerations show that efforts should be directed toward better matching of the preamplifier to the probe circuit rather than cooling the preamplifier circuit. If we can achieve noise matching and impedance matching at the same time, then cooling the preamplifier becomes of little value. As a practical design example, consider the amplifier circuit in Fig. 2. The series capacitor C, either matches the preamplifier to the 50-Q input from the probe to obtain maximum power transfer or transforms the 50-Q input to have a real value of R,, (as seen by the FET) to obtain maximum input SNR. Usually these two conditions require different values of C1. To estimate the magnitude of the transformed resistance, consider the MGF 1402 FET (Mitsubishi) that might be used in the design of a low-noise preamplifier. The transconductance of the component at 10 mA drain current is G, = 45 mS, and the gain-bandwidth product ft in the same biasing condition is approximately 30 GHz as obtained from the specification sheets. For our operating frequency of 360 MHz, we obtain from Eq. (6) an R,, of 3 kQ. A transformation ratio of 60 is thus required from the matching circuit. This type of operation occurs at the expense of the gain because, in general, optimum power coupling is not achieved with the same parameters as those required for minimum noise temperature. For a typical amplifier input circuit, Fig. 2, the matching input circuit of the amplifier containing C, , C,, and L, should provide an impedance transformation that makes the line impedance appear to the FET as R,, at the frequency of interest. The total complex
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Fig. 2. Typical NMR preamplifier
circuit.
283
in
admittance Y of the source as seen from the gate of the FET is given by
y=jwc,+
jwcl
1 7
+
JWLl
1 + jwCIR,
’
By setting the real part of the right-hand side equal to l/R,, the desired optimum noise admittance, we can solve for the matching capacitance C1, as 1
c, =
noise performance. As was shown, this performance will not be significantly improved by cooling the preamplifier, and F1/F2 in Eq. (3) remains approximately equal to unity for a well-designed preamplifier.
Wa which, in general, does not correspond to the matching impedance required to achieve maximum power transfer. We will see, however, that with the appropriate choice of R,, through selection of the bias point, both constraints can satisfactorily be fulfilled. Using Eq. (8) and the value for the optimal source resistance determined for the FET (3 kQ), an optimal noise matching capacitance of 1.15 pF is obtained. This value is very close to the matching capacitance of approximately 1 pF required for source impedance matching as determined experimentally. With this matching capacitance value, the amplifier input impedance is approximately 50 fl and satisfies the condition for maximum power transfer. This suggests that to achieve optimum noise-gain tradeoff, the FET bias point should be selected such that Eq. (6) and Eq. (8) yield a capacitance value of approximately 1 pF. For the Mitsubishi MGF 1402 FET, this corresponds to approximately 10 mA of drain current. Equation (5) shows that the dependence of the noise figure on the input source impedance is not sharp, being given by the slowly varying function (x + l/x), where x = RJR,. Therefore, it is possible to satisfy the powermatching condition and still maintain an excellent
METHODS
NMR experiments were performed at the Francis Bitter National Magnet Laboratory, Cambridge, MA, USA. A 7.1-cm bore, 8.46-T superconducting magnet (Oxford Instruments) interfaced to a home-built spectrometer was used with home-built gradient waveform generators and unshielded orthogonal gradients.4 To verify the SNR improvement predicted by Eq. (3), a cooled probe assembly was constructed. A standard tapped parallel resonance circuit (C’ and C2 = 0.8-8 pF) was mounted on copper-clad circuit board material and housed in a 7.dmm-thick nylon insulated chamber, enclosed by an aluminum rf shield. Extended capacitor shafts were used to allow retuning of the circuit at each temperature. The entire resonance circuit with the exception of the microcoil was maintained between 150 and 300 K using nitrogen gas. The sample chamber was insulated from the cooled circuit chamber and maintained at room temperature using warmed nitrogen gas. The temperature in both chambers was monitored with thermocouples. The temperature of the microcoil varied along its length. At the contacts of the coil to the tuning capacitors, the coil was at the temperature of the cooled circuit chamber (150-300 K). Within the sample chamber (29.3 K) where heat transferred by convection, the coil temperature was higher. An approximately 50-pm gap was added between the sample and coil to allow for an adequate gas flow rate to be established to maintain the sample above freezing (Fig. 1). This approach has the advantage that there is minimal filling factor loss due
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to insulation layers placed between the coil and the sample. The disadvantage is that the required high flow rates produced mechanical motion of the sample and microcoil. The microcoils were constructed for individual samples using three turns of copper wire (150-500 pm diameter) wound on micropipettes (300-1000 pm o.d.) containing the sample. The coils were wound under an optical microscope. For SNR measurements, a 1.O-mmo-d. pipette was used. Typically, 90” pulse widths were 4-6 psec at 2.5 W, The probe assembly fit inside the home-built orthogonal imaging gradients with a 34mm inside diameter. Allowances for external probe tuning were incorporated into the probe design. The probe circuit resonant frequency decreased with decreasing temperature and was retuned at each temperature using the extended capacitor shafts. The total variation over the 150-K range was approximately 2.1 MHz. A relatively rapid frequency shift occurred over a few degrees around 223 K. We did not investigate the origin of this more rapid frequency shift. An approximately IO-min period was allowed for stabilization at each temperature prior to data collection. No variation in circuit tuning was noted over the course of data collection. For SNR measurements, data was acquired at 5 kHz. A single low tip angle excitation was used to ensure adequate noise digitization by reducing the signal amplitude to no more than 150 times the noise amplitude. With larger tip angles, the signal was several thousand times the noise that would represent less than 1 bit in the g-bit analog-to-digital converter. The Fourier transform of the free induction decay obtained in the absence of gradients was integrated over 600 Hz to obtain the signal. The noise was determined from the calculated root mean square deviation in a 600-Hz region of the spectrum 1 kHz off resonance. Six signal and noise values were obtained at each probe temperature. Imaging experiments were performed using a 3D modification of the zeugmatography method first proposed by Kumar et al. 25 Gradient values between 10 and 100 G/cm were used with bandwidths ranging from 5 to 20 kHz. TE was typically 8 msec, and phaseencoding time t, was 4 msec. Following 3D Fourier transformation of the raw data, the image array was transferred to a Silicon Graphics Iris 4D121OGTX computer for display using commercial display software. No filtering or postprocessing was done on the raw data. The robust green algae Nitella and Micrasterias were chosen as model systems for imaging. Nitella are readily available and range in size between 100 and 500
pm. Additionally, Nitella has a remarkable active internal circulation driven by photosynthetic energy, which was paralyzed by the absence of light. The smaller ellipsoidal Micrasterias are quiescent and available in major diameters of 50-150 pm. The cells were placed in distilled water and sealed in glass sample tubes. No bulk movement of the cells within the sample tubes was noted when observed overnight under a videomicroscope. RESULTS The variation of the SNR with probe circuit temperature was measured at four temperatures between 150 and 300 K. The values of SNR at the reduced tip angle ranged from 88 (t 10) to 140 (+ 25). The ratios are pIotted together with predicted results in Fig. 3. The ratio fi/f2 from Eq. (3) is plotted where f, is computed for a microscopy probe cooled to various temperatures Tel, (QU/Qr)r = 1. For each case F, = F2 and T,, = T,, = 290 K. In curve a, fi is computed for an uncooled microscopy probe [( QJQ& = 11. This is the condition measured experimentally. Curve b is a comparison to a standard MRI probe [( QllQL)2 = IO]. In curve b, a factor of 3 improvement is achieved without cooling due to the effect of coil loading in the large MRI probe. Further improvements are obtained by cooling the probe circuitry as indicated. Curve c shows the ratio of SNRs for two MRI coils [(Q,/ QL), = ( QUQL)2 = 101 where one is cooled; little improvement in SNR is obtained because the dominant
- 5b
100
150
200
Probe Circuit Temperature
250
300
(K)
Fig. 3. Predicted effect of probe cooling on SNR from Eq. (3), comparing the ratios of SNRs of (curve a) a cooled microscopy probe to an uncooled microscopy probe, (QJ QL) 1 = ( Qu/QL)z = 1; (curve b) a cooled microscopy probe, ( QU/QL), = 1, to a standard MRI probe, ( QU/QL)z = 10; and (curve c) cooled and uncooled MRI probes, ( QU/QL), = (Qu/QL)2 = 10. Actual data points from a cooled 5O@pmdiameter copper microcoil probe circuit are also shown.
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Table 1. Combined effects on overall SNR
Arl bm) 25 5 1
1.6 x 1O-5 1.2 x 1o-7 10-9
100 100 100
circuit loading is due to a room temperature load. The reduced coil resistance with cooling is the dominant effect. The curves all represent probe cooling with a room temperature sample. Table 1 gives a summary of the combined effects on the SNR of all factors discussed. For the purposes of illustration and order of magnitude estimates, the predicted ratio of SNR per voxel in microscopy at resolutions of 25, 5, and 1 pm is compared with clinical MRI at 1 T with resolution of 1 mm. Under optimal conditions, to achieve an identical SNR per voxel in NMR microscopy at Ar = 1 pm as obtained in MRI imaging at Ar = 1000 pm requires an additional gain in SNR of 103. An enormous amount of signal averaging is one possible means. Example images of green algae cells are shown in Figs. 4 and 5. A light micrograph of a single Mcrasterias cell is shown in Fig. 4A together with a length scale. A 3D NMR image was obtained using a microcoil wound on an 800~pm-o.d. micropipette with 400pm i.d. The cell was drawn into the micropipette and suspended in saline. After approximately 30 min it rested on the bottom of the pipette and remained essentially motionless as confirmed by sequential light micrographs. To reduce the diffusive motion of water protons in the NMR image, the temperature of the sample was reduced to 283 K. A full 3D image was obtained from 64 and 32 y- and z-phase-encoding steps, respectively, with 32 signal averages each and a recycle delay of 0.4 sec. A TE of 8 msec was used giving an overall TL weighting to the image. The frequencyencoding gradient was approximately 50 G/cm, and 256 time domain points were sampled at a rate of 20 kHz. In Fig. 4B one 12-pm slice from the 3D data set is shown (scale is approximately two times that of Fig. 4A). An ellipsoidal form of reduced signal intensity is observed, indicating the cell membrane. We believe the rings of increased intensity around the membrane correspond to water protons with shortened TI from their proximity to the membrane surface. Minimal proton signal intensity is detected from
1 1 1
40 200 1000
2 5 10
Z 10-l -10-2 -10-3
the cell center, likely due to decreased abundance and extremely short T2’s within the dense central organelles. The resolution in plane was approximately 8 x 6 pm. Projection images were obtained of a second algal species using a cooled probe. Figure 5A is a light micrograph of a dividing Nitella. The same cell cluster was used for NMR imaging. Figure 5B (left) shows a spin-echo projection image of Nitella acquired in 2.2 min using only the x and z gradients. The y gradient was turned off, and data were acquired with 64 zphase-encoding steps using a recycle delay of 0.5 set and four signal averages. The probe and sample were maintained at 297 K. The projection image is the NMR equivalent of a transmission light micrograph where the image represents the NMR signal integrated over a line of constant y. In the NMR image the axis of the Nitella is rotated 90” compared with the Iight micrograph, and the length scale is approximately identical. The cell is observed to be dividing and is sending out filamentous extensions typical of Chlorophyta cell division. The cell walls are clearly visualized as regions of decreased intensity, and as before a perimembrane signal enhancement is seen. After the probe was cooled to 213 K, the NMR image on the right of Fig. 5B was obtained under otherwise identical conditions. Though the SNR was modestly improved, considerable blurring is noted due to mechanical motion of the sample coil in the rapid warm nitrogen gas stream within the sample area required to maintain the sample at room temperature. This technical problem will be addressed in future work. DISCUSSION Historically, statements of limits on NMR imaging have proved to be shortsighted. Proton imaging of the human body in fields over 0.3 T was predicted early on to be impossible.tg SNR will ultimately limit spatial resolution in NMR microscopy, and the trends noted
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Fig. 4. Microscopic images of a single green alga cell (Micrasterias). (A) A light micrograph with a scale demonstrating the contour of the spiny disk-shaped cell wall. A complete 3D NMR image data set was then obtained using a spin-echo sequence with 16 signal averages. The echo time
was 8 msec and TR was 400 msec; 64 and 32 y- and z-phase encoding steps were used respectively. (B) A 12-pm slice from the 3D data set at approximately twice the scale of the light micrograph. The oval ring of decreased signal intensity corresponds to the cell wall. The intensity of the image from the central region of the cell, which contains the nucleus, chloroplasts, and other organelles, is greatly reduced in this Lrrweighted image.
in Table 1 provide a useful guide for practical expectations. One cannot expect the same high-quality images seen in MRI of human brains to be produced from single cells. Improved filling factor and probe noise reduction are the most apparent means for improving SNR. Our studies indicate that the most significant gains in SNR can be obtained by maximizing the inductive coupling of the sample to the probe. Practically, the manufacturing of microcoils poses major challenges,
with significant room for improvement. One must be careful in choosing the material for the microcoils to avoid susceptibility artifacts. We have noted large artifacts on several occasions from localized impurities in the coil wire. Additionally, attention must be given to the reduced surface area and requisite increase in resistance of such coils. There have been reports of efforts to use high-temperature superconducting materials for probe conductors in medical MRI coils. The theoretical justification for this is given by Eq. (3),
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ulOOpm (4
(B) Fig. 5. Microscopic projection images of the dividing green alga Nitella. (A) A light micrograph demonstrating the budding of progency cells from the main cell stem. (B) An NMR projection image of the same cell cluster obtained (left) using only the x and z gradients with the probe maintained at 297 K. The budding extensions of the dividing cell are clearly visualized as in the light micrograph (note that the sample axis was rotated 900). The probe assembly was cooled to 223 K and an NMR image obtained under otherwise identical conditions (right). Though the SNR improved modestly, the physical motion of the sample due to the high gas flow rate required to keep the sample at 297 K caused a reduction in resolution.
whereby an increase in SNR by the square root of the coil resistance is noted. Note that this improvement will be realized even in the presence of the significant coil loading by the patient [( QU/QL), = ( Qu/QL)2 = 101. Probe cooling offers an additional means of improving SNR in NMR microscopy. Our data is consistent with the theoretical predictions over a relatively small temperature range; however, we would expect the agreement to continue to significantly lower temperatures. Major technical and design problems such as mechanical stability, which limited the spatial res-
olution in our microscopic images of cells using the cooled assembly, have yet to be overcome. Improved cryogenic and thermal design is also needed to allow further reduction in circuit temperature while maintaining the appropriate sample temperature environment. Though the fundamental limit is SNR, the major practical hurdles to reliable NMR microscopy are (1) mechanical motion of the apparatus, (2) instrument stability, and (3) sample viability. These factors will prevent indefinite signal averaging and need to be seriously considered in the engineering design of microscopic imaging systems.
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Acknowledgmenfs-The authors acknowledge and thank the scientific staff of the Comprehensive NMR Facility (supported by NIH Grant RRO0995) at the Francis Bitter National Magnet Laboratory, Cambridge, MA, for their technical support. Also, D.J. Ruben and J.W. Wrenn provided extensive technical support and many helpful discussions. A. Tannus and L.J. Neuringer’s reviews of the manuscript were greatly appreciated. This work was supported in part by the Whitaker Health Sciences Fund and an NSF PYI award (DIR-9057151). REFERENCES 1. Mansfield, P.; Grannel, P.K. “Diffraction” and microscopy in solids and liquids by NMR. Phys. Rev. B. 12:
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15:6:815-824; 1988. 12. Callaghan, P.T.; Eccles, C.D. Sensitivity and resolution in NMR imaging. J. Magn. Reson. 71~426-445; 1987. 13. Hennessy, M.J.; Parsons, D. What is the physical limit of resolution of magnetic resonance microscopy (MRM). Abstracts. 4th Annual Meeting of Society of Magnetic Resonance in Medicine, London. 1422-1423; 1985. 14. McFarland, E.W.; Mortara, A. Subcellular NMR microscopic imaging. Abstracts. 9th Annual Meeting of Society of Magnetic Resonance in Medicine, New York. 1127; 1990. E.W.; Mortara, A. Three-dimensional 15. McFarland, NMR microscopy: Pushing the SNR limit with temperature and microcoils. Abstracts. Experimental Magnetic Resonance Conference, St. Louis; 1991. 16. McFarland, E.W. Time independent t point spread function for NMR microscopy. Mugn. Reson. Imaging 10: 1; 1991. 17. Abragam, A. The Principles of Nuclear Magnetism. Oxford: Clarendon Press; 1961. 18. Hoult, D.I.; Richards, R.E. The signal-to-noise ratio of the nuclear magnetic resonance experiment. J. Magn.
Reson. 24:71; 1976. 19. Hoult, D.I.; Lauterbur, P.C. The sensitivity of the zeugmatographic experiment involving human samples. J.
Magn. Reson. 341425-433; 1979. 20. Edelstein, W.A.; Glover, G.H.; Hardy, C.J.; Redington, R.W. The intrinsic signal-to-noise ratio in NMR imaging. Magn. Reson. Med. 3:604-618; 1986. 21. Carr, H.Y.; Purcell, E.M. Effects of diffusion on free precession in nuclear magnetic resonance experiments.
Phys. Rev. 63:3:630-638; 1954. 22. Styles, P.N.; Soffe, F.; Scott, C.A.; Cragg, D.A.; Row, F.; White, D.J.; White, P.C.J. A high-resolution NMR probe in which the coil and preamplifier are cooled with liquid helium. J. Mugn. Reson. 34:397-404; 1984. 23. Styles, P.N.; Soffe, F.; Scott, C.A. An improved cryogenically cooled probe for high-resolution NMR. J.
Magn. Reson. 84:2:376-378; 1989. 24. Robinson, F.N.H. Noise and Fluctuations in Electronic Devices and Circuits. Oxford: Clarendon Press; 1973. 25. Kumar, A.; Welti, D.; Ernst, R.R. Imaging of macroscopic objects by NMR Fourier zeugmatography. Natur-
wissenschaft, 62:34; 1.975.
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0 Original Contribution THREE-DIMENSIONAL NMR MICROSCOPY: IMPROVING SNR WITH TEMPERATURE AND MICROCOILS E.W.
MCFARLAND
AND
A.
MORTARA
of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA, and Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA, USA
Department
It is widely held that the spatial resolution achievable by NMR microscopic imaging is limited in biological systems by diffusion to approximately l-5 Cm. However, these estimates were developed for specific imaging techniques and represent practical rather than fundamental limits. NMR imaging is limited by the signal-to-noise ratio (SNR). Diffusion effects on spatial resolution can be made arbitrarily small in principle by increasing the gradient strength. The exponential signal attenuation from random spin motion in a gradient, however, will reduce the signal far below the noise level when the voxel size is reduced much below 5pm. Two factors can be optimized to improve the SNR: (1) the inductive linkage between microscopic samples and the detection apparatus and (2) the temperature of the rf probe. In this work, the filling factor was optimized using inductors with diameters less than 1 mm. It is furthermore shown that probe circuit cooling results in significant improvements in SNR, whereas cooling of the preamplifier is of little value when proper noise matching between the resonant circuit and preamplifier is accomplished. Using three-dimensional Fourier imaging techniques, we have obtained images of singlecell organisms with spatial resolution of approximately 6 pm. Practical limitations include mechanical stability of the apparatus, thermal shielding between the sample and probe, and the magnetic susceptibility of the sample. Keywords:
NMR microscopy;
INTRODUCTION
AND
Signal-to-noise
ratio; Cryogenics;
In practice, the magnetic component of a large number of coherent photons is detected by induction. For this method of detection, the SNR has been calculated by many investigators.“-” In NMR microscopy of small samples (d < 1 mm diameter), there is negligible loading of a room temperature coil by the sample, and the original SNR analysis of Hoult and Richards is applicable. I8 The signal detected in a coil surrounding a sample of dimension d, consisting of (r~)~ volume elements, each of dimension Ar, is well understood. Though several general forms might be used for the induced voltage SNR obtained from the nuclear induction, we will use the expression:
THEORY
Since the advent of NMR imaging, there have been ongoing efforts to improve the spatial resolution to the subcellular level.‘-‘5 It is the reduction in SNR from the reduced voxel size that fundamentally limits spatial resolution. At present, the practical limit is approximately 5-10 hrn. The effects of diffusion and bulk motion of nuclei on the NMR signal are well known and are an inconvenience; however, they do not create a fundamental limit to the spatial resolution.r5,i6 We are interested in microscopy of singlecell preparations where coherent motion and regional magnetic susceptibility differences can be neglected. In this regime, several of the rf detection assumptions of medical NMR imaging are no longer valid. In particular, for microsamples the dominant source of noise is no longer a priori the object. In this communication, methods to improve the SNR in practical microscopic applications are described, together with examples from living systems. RECEIVED 7/2/9l; ACCEPTED lO/ 14191. Address correspondence to E.W. McFarland,
Preamplifier.
SNR - (Ar)3py3H;(bw)-1’2
7 i
1
Xf(Tp, T,,R,,R,,F)W(D)~total
time
(1)
where p is the nuclear spin density; y is the nuclear gyromagnetic ratio, Ho is the main field strength, bw is of Chemical and Nuclear Engineering, University of California, Santa Barbara, CA 93106. email: [email protected].
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the bandwidth, and (HI/i) is the magnetic field produced in the volume per unit coil current. f(T,, T,, R,, R,,F) is a function of the probe and sample temperatures TP and T,, their effective resistances, R, and R,, and the amplifier noise figure F. This factor will be discussed in detail below. The factor W(D) is introduced here to represent the reduction in signal intensity due to spin diffusion.” Reducing the resolution element obtainable with a clinical MRI system (Ar approximately 1 mm) to Ar = 1 pm results in a reduction in SNR of approximately 109, simply due to the reduction in the number of spins in the voxel generating the signal. The challenge for the NMR microscopist is to recover as much of that IO9 SNR deficit as possible. The system to be imaged will determine the first several terms in Eq. (1). Assuming we are interested in imaging the ubiquitous H’ nucleus in a small liquid system, a high field strength will be chosen. 10-T magnets are readily available, and the SNR deficit can be reduced in these fields by a factor of 10P2, compared with 1-T clinical MRI systems. The reduction in relaxation contrast at higher fields will be ignored for this comparison. The image bandwidth, bw, involves several factors, and because of considerations of data acquisition time, gradient strength, and field homogeneity, typical values are between 3 and 10 kHz for both MRI and NMR microscopy. The optimal bw has been given by Callaghan and Eccles for an image matrix of size n as r~/aT~.‘~ The bandwidth is predicted to remain constant for any resolution as long as the matrix size remains constant. In fact, for microscopy, diffusion will dominate the signal loss and the broadening of the linewidth from a single volume element. In a spin system of diffusion coefficient D, the minimum gradient strength G is related to the required resolution Ar by: I6 Ar=83
JNlnPl)* 3yG
*
This expression can be solved for the required gradient. The image bandwidth for an object of total dimension d = nAr is then: bw=ynArG=,,ar[DF(:)l]
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terms in Eq. (1). These are essentially the only experimentally variable factors. Filling Factor Improvement The term HI/i reflects the magnetic flux coupling between the NMR photons and the rf receiving coil. I8 The term HI/i is typically maximized by reducing the radius of the coil to approximately that of the sample, thus optimizing the filling factor.” The ideal coil diameter will be approximately that of the sample, d = nAr, where n is the size of the image array. For our studies, cells are contained in micropipettes with diameters of approximately 100-1000 pm (Fig. 1). In the most favorable case, the improvement in HI/i compared with the MRI system will be the inverse of their respective voxel sizes when identical array sizes are used. The lo9 SNR deficit is readily reduced by lo-’ and lop3 on the basis of the field strength and small sample probe geometry, respectively. The remaining factor of 104, however, is an enormous deficit in SNR, and further work is necessary to improve the system for useful microscopic imaging. RF Detector Cooling The other variable under the control of the NMR microscopist is the termf(T,, T,, R,, R,, F) in Eq. (1). As is well known, the noise in NMR is due to thermal noise from the sample and probe circuits.“-I9 The term f ( TP, T,, R,, R,, F) contains the dependence of the SNR on the sample and probe absolute temperatures and their effective resistances. Additionally, the Curie law dependence of the signal on temperature is included. The thermal noise of a given resistance varies as (RT) 1’2. Noise is reduced if resistance and/or temperature are reduced. Unfortunately, liquid biological samples studied in vivo are limited to temperatures T, > 273 K. It is possible to cool the sample and probe circuit to different temperatures, T, and T,. In this case, the model of the probe circuit noise as a series combination of two independent noise generators may be used. One source is due to the actual probe resistance with a noise power of R,T,, and the other is due to the effective series resistance of the sample, R,, with a noise power of R,T,. An estimate of the improvement in SNR that can be achieved by lowering the temperature of the sample and/or coil is given by
.
1
SNR 4 T:(R,T, For our work, we observed the H’ nucleus at the highest field available to us (8.4-T). Efforts were focused on maximizing the H, /i and f (T,, T,, RP, R,, F)
+ R,K)
(2)
where the TsP’ Curie law dependency is included together with the resistive noise power.22 Experimen-
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Fig. 1. Schematic of single-cell probe. The coil circuit is cooled with nitrogen gas at T, (150-300 K). The sample temperature is maintained at T, = 283 K by a separate, warmer, gas stream in gap between the cooled conductors and the sample holder.
tally, R, can be determined by measurement of the circuit Q with the sample in place [ QL = wL/( R, + R,)] and after removing the sample, (Qu = wL/R,). The change in the coil inductance, L, with loading is negligible for small samples. The ratios of the factor f(T,, T,, R,, R,, F) for different temperature conditions can be written using the expressions for the experimentally determined Q’s in Eq.(2) to compare two probe configurations.‘4
_fr
SNRI SNRz
-fi
can be both from a direct reduction in thermal energy and by a reduction in circuit resistance. Above superconducting temperatures, the ohmic resistance of the inductor is well known. For a solid copper wire coil, R, depends on the coil radius r, the wire diameter a, the resistivity p, the number of turns N, and the skin depth 6,. For temperatures above the critical temperature, the decrease in skin depth with decreased rebalances the direct sistivity [6, - (p)‘j2] partially reduction in resistivity with temperature and
R,=p(T)s -m-v++cu(T-273K). s
(3) For microscopy using microcoils (r < 1 mm), QJQL is approximately 1, whereas for large medical MRI systems operating at 1 T, QU/QL is between 5 and 10. The ratio of the coil-to-sample temperature is therefore much more important in the microscopy system. Equation (3) indicates that an SNR increase is obtained by cooling the resonant circuit itself relative to the sample when the coil loading is weak. The increase
For copper, Q! = 0.004 K-l, and the overall effect on Eq. (3) from the ratio of resistances is weak. As materials research progresses and high-critical-temperature materials become available, the resistance dependence of Eq. (3) can be more fully exploited. However, at present the thermal shielding requirements required for superconducting detectors will limit the gains in noise reduction by lost filling factor. The direct noise power reduction will largely determine the benefit in nonsuperconducting coils.
Preamplifier cooling effects. The preamphfier noise figure F is typicaIIy deiined in terms of noise power ratios at the input and output of the device. The depen-
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dency of the NMR signal voltage SNR on preamplifier noise figure is approximately F-l”. The temperature dependence of the ratio of the noise figures for a preamplifier at two different temperatures (F,/F, ) is less explicit for preamplifiers designed using low-noise field effect transistors (FETs). It has been reported by Styles that improvements in SNR can be achieved by cooling the preamplifier as well as the probe circuit.22*23 To compare the cooled and uncooled preamplifiers, the ratio of the noise figures can be expressed in terms of equivalent noise temperatures as
F(C)
-
=
F(T,)
Ts
+
Tn2
Ts
+
Tn,
(4)
where T, is the signal source the noise temperature of the ture T, . In the most general fier noise temperature takes
temperature, and T,, is preamplifier at temperasituation, the FET amplithe form:24
where w
V
=24kT 3 G,
is the noise power spectral density of the amplifiergenerated noise, G, is the transconductance of the FET, T is the FET temperature, R, is the actual source resistance, and R,, is the optimal source resistance obtained by setting: s_ 6’R, -
and solving
0
for R, = R,,
(6) where fi = G,/2aC, is the gain-bandwidth product of the FET and C, its gate capacitance. This value represents the optimal source resistance that the FET gate must see in order to achieve minimum noise figure. If properly matched noisewise, the preamplifier will have a minimum noise temperature:25
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l/2
0 0 -
3
5
I
T
for
fcfr
.
(7)
Equation (7) shows that the noise temperature is only a small fraction of the amplifier’s temperature T if the operating frequency f is low compared with the transistor gain-bandwidth product ft. Additionally, cooling the preamplifier will yield only a marginal noise figure improvement unless the source resistance is very different from the desired R,,. For example, for an fi of 3 GHz and an operating frequency of 300 MHz, cooling the preamplifier from 293 to 163 K under noise-matched conditions yields a decrease in noise temperature of less than 11 K. If a transistor designed for higher frequency is used, say with f, = 30 GHz, this improvement is reduced to less than 1.1 K! These considerations show that efforts should be directed toward better matching of the preamplifier to the probe circuit rather than cooling the preamplifier circuit. If we can achieve noise matching and impedance matching at the same time, then cooling the preamplifier becomes of little value. As a practical design example, consider the amplifier circuit in Fig. 2. The series capacitor C, either matches the preamplifier to the 50-Q input from the probe to obtain maximum power transfer or transforms the 50-Q input to have a real value of R,, (as seen by the FET) to obtain maximum input SNR. Usually these two conditions require different values of C1. To estimate the magnitude of the transformed resistance, consider the MGF 1402 FET (Mitsubishi) that might be used in the design of a low-noise preamplifier. The transconductance of the component at 10 mA drain current is G, = 45 mS, and the gain-bandwidth product ft in the same biasing condition is approximately 30 GHz as obtained from the specification sheets. For our operating frequency of 360 MHz, we obtain from Eq. (6) an R,, of 3 kQ. A transformation ratio of 60 is thus required from the matching circuit. This type of operation occurs at the expense of the gain because, in general, optimum power coupling is not achieved with the same parameters as those required for minimum noise temperature. For a typical amplifier input circuit, Fig. 2, the matching input circuit of the amplifier containing C, , C,, and L, should provide an impedance transformation that makes the line impedance appear to the FET as R,, at the frequency of interest. The total complex
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Fig. 2. Typical NMR preamplifier
circuit.
283
in
admittance Y of the source as seen from the gate of the FET is given by
y=jwc,+
jwcl
1 7
+
JWLl
1 + jwCIR,
’
By setting the real part of the right-hand side equal to l/R,, the desired optimum noise admittance, we can solve for the matching capacitance C1, as 1
c, =
noise performance. As was shown, this performance will not be significantly improved by cooling the preamplifier, and F1/F2 in Eq. (3) remains approximately equal to unity for a well-designed preamplifier.
Wa which, in general, does not correspond to the matching impedance required to achieve maximum power transfer. We will see, however, that with the appropriate choice of R,, through selection of the bias point, both constraints can satisfactorily be fulfilled. Using Eq. (8) and the value for the optimal source resistance determined for the FET (3 kQ), an optimal noise matching capacitance of 1.15 pF is obtained. This value is very close to the matching capacitance of approximately 1 pF required for source impedance matching as determined experimentally. With this matching capacitance value, the amplifier input impedance is approximately 50 fl and satisfies the condition for maximum power transfer. This suggests that to achieve optimum noise-gain tradeoff, the FET bias point should be selected such that Eq. (6) and Eq. (8) yield a capacitance value of approximately 1 pF. For the Mitsubishi MGF 1402 FET, this corresponds to approximately 10 mA of drain current. Equation (5) shows that the dependence of the noise figure on the input source impedance is not sharp, being given by the slowly varying function (x + l/x), where x = RJR,. Therefore, it is possible to satisfy the powermatching condition and still maintain an excellent
METHODS
NMR experiments were performed at the Francis Bitter National Magnet Laboratory, Cambridge, MA, USA. A 7.1-cm bore, 8.46-T superconducting magnet (Oxford Instruments) interfaced to a home-built spectrometer was used with home-built gradient waveform generators and unshielded orthogonal gradients.4 To verify the SNR improvement predicted by Eq. (3), a cooled probe assembly was constructed. A standard tapped parallel resonance circuit (C’ and C2 = 0.8-8 pF) was mounted on copper-clad circuit board material and housed in a 7.dmm-thick nylon insulated chamber, enclosed by an aluminum rf shield. Extended capacitor shafts were used to allow retuning of the circuit at each temperature. The entire resonance circuit with the exception of the microcoil was maintained between 150 and 300 K using nitrogen gas. The sample chamber was insulated from the cooled circuit chamber and maintained at room temperature using warmed nitrogen gas. The temperature in both chambers was monitored with thermocouples. The temperature of the microcoil varied along its length. At the contacts of the coil to the tuning capacitors, the coil was at the temperature of the cooled circuit chamber (150-300 K). Within the sample chamber (29.3 K) where heat transferred by convection, the coil temperature was higher. An approximately 50-pm gap was added between the sample and coil to allow for an adequate gas flow rate to be established to maintain the sample above freezing (Fig. 1). This approach has the advantage that there is minimal filling factor loss due
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to insulation layers placed between the coil and the sample. The disadvantage is that the required high flow rates produced mechanical motion of the sample and microcoil. The microcoils were constructed for individual samples using three turns of copper wire (150-500 pm diameter) wound on micropipettes (300-1000 pm o.d.) containing the sample. The coils were wound under an optical microscope. For SNR measurements, a 1.O-mmo-d. pipette was used. Typically, 90” pulse widths were 4-6 psec at 2.5 W, The probe assembly fit inside the home-built orthogonal imaging gradients with a 34mm inside diameter. Allowances for external probe tuning were incorporated into the probe design. The probe circuit resonant frequency decreased with decreasing temperature and was retuned at each temperature using the extended capacitor shafts. The total variation over the 150-K range was approximately 2.1 MHz. A relatively rapid frequency shift occurred over a few degrees around 223 K. We did not investigate the origin of this more rapid frequency shift. An approximately IO-min period was allowed for stabilization at each temperature prior to data collection. No variation in circuit tuning was noted over the course of data collection. For SNR measurements, data was acquired at 5 kHz. A single low tip angle excitation was used to ensure adequate noise digitization by reducing the signal amplitude to no more than 150 times the noise amplitude. With larger tip angles, the signal was several thousand times the noise that would represent less than 1 bit in the g-bit analog-to-digital converter. The Fourier transform of the free induction decay obtained in the absence of gradients was integrated over 600 Hz to obtain the signal. The noise was determined from the calculated root mean square deviation in a 600-Hz region of the spectrum 1 kHz off resonance. Six signal and noise values were obtained at each probe temperature. Imaging experiments were performed using a 3D modification of the zeugmatography method first proposed by Kumar et al. 25 Gradient values between 10 and 100 G/cm were used with bandwidths ranging from 5 to 20 kHz. TE was typically 8 msec, and phaseencoding time t, was 4 msec. Following 3D Fourier transformation of the raw data, the image array was transferred to a Silicon Graphics Iris 4D121OGTX computer for display using commercial display software. No filtering or postprocessing was done on the raw data. The robust green algae Nitella and Micrasterias were chosen as model systems for imaging. Nitella are readily available and range in size between 100 and 500
pm. Additionally, Nitella has a remarkable active internal circulation driven by photosynthetic energy, which was paralyzed by the absence of light. The smaller ellipsoidal Micrasterias are quiescent and available in major diameters of 50-150 pm. The cells were placed in distilled water and sealed in glass sample tubes. No bulk movement of the cells within the sample tubes was noted when observed overnight under a videomicroscope. RESULTS The variation of the SNR with probe circuit temperature was measured at four temperatures between 150 and 300 K. The values of SNR at the reduced tip angle ranged from 88 (t 10) to 140 (+ 25). The ratios are pIotted together with predicted results in Fig. 3. The ratio fi/f2 from Eq. (3) is plotted where f, is computed for a microscopy probe cooled to various temperatures Tel, (QU/Qr)r = 1. For each case F, = F2 and T,, = T,, = 290 K. In curve a, fi is computed for an uncooled microscopy probe [( QJQ& = 11. This is the condition measured experimentally. Curve b is a comparison to a standard MRI probe [( QllQL)2 = IO]. In curve b, a factor of 3 improvement is achieved without cooling due to the effect of coil loading in the large MRI probe. Further improvements are obtained by cooling the probe circuitry as indicated. Curve c shows the ratio of SNRs for two MRI coils [(Q,/ QL), = ( QUQL)2 = 101 where one is cooled; little improvement in SNR is obtained because the dominant
- 5b
100
150
200
Probe Circuit Temperature
250
300
(K)
Fig. 3. Predicted effect of probe cooling on SNR from Eq. (3), comparing the ratios of SNRs of (curve a) a cooled microscopy probe to an uncooled microscopy probe, (QJ QL) 1 = ( Qu/QL)z = 1; (curve b) a cooled microscopy probe, ( QU/QL), = 1, to a standard MRI probe, ( QU/QL)z = 10; and (curve c) cooled and uncooled MRI probes, ( QU/QL), = (Qu/QL)2 = 10. Actual data points from a cooled 5O@pmdiameter copper microcoil probe circuit are also shown.
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Table 1. Combined effects on overall SNR
Arl bm) 25 5 1
1.6 x 1O-5 1.2 x 1o-7 10-9
100 100 100
circuit loading is due to a room temperature load. The reduced coil resistance with cooling is the dominant effect. The curves all represent probe cooling with a room temperature sample. Table 1 gives a summary of the combined effects on the SNR of all factors discussed. For the purposes of illustration and order of magnitude estimates, the predicted ratio of SNR per voxel in microscopy at resolutions of 25, 5, and 1 pm is compared with clinical MRI at 1 T with resolution of 1 mm. Under optimal conditions, to achieve an identical SNR per voxel in NMR microscopy at Ar = 1 pm as obtained in MRI imaging at Ar = 1000 pm requires an additional gain in SNR of 103. An enormous amount of signal averaging is one possible means. Example images of green algae cells are shown in Figs. 4 and 5. A light micrograph of a single Mcrasterias cell is shown in Fig. 4A together with a length scale. A 3D NMR image was obtained using a microcoil wound on an 800~pm-o.d. micropipette with 400pm i.d. The cell was drawn into the micropipette and suspended in saline. After approximately 30 min it rested on the bottom of the pipette and remained essentially motionless as confirmed by sequential light micrographs. To reduce the diffusive motion of water protons in the NMR image, the temperature of the sample was reduced to 283 K. A full 3D image was obtained from 64 and 32 y- and z-phase-encoding steps, respectively, with 32 signal averages each and a recycle delay of 0.4 sec. A TE of 8 msec was used giving an overall TL weighting to the image. The frequencyencoding gradient was approximately 50 G/cm, and 256 time domain points were sampled at a rate of 20 kHz. In Fig. 4B one 12-pm slice from the 3D data set is shown (scale is approximately two times that of Fig. 4A). An ellipsoidal form of reduced signal intensity is observed, indicating the cell membrane. We believe the rings of increased intensity around the membrane correspond to water protons with shortened TI from their proximity to the membrane surface. Minimal proton signal intensity is detected from
1 1 1
40 200 1000
2 5 10
Z 10-l -10-2 -10-3
the cell center, likely due to decreased abundance and extremely short T2’s within the dense central organelles. The resolution in plane was approximately 8 x 6 pm. Projection images were obtained of a second algal species using a cooled probe. Figure 5A is a light micrograph of a dividing Nitella. The same cell cluster was used for NMR imaging. Figure 5B (left) shows a spin-echo projection image of Nitella acquired in 2.2 min using only the x and z gradients. The y gradient was turned off, and data were acquired with 64 zphase-encoding steps using a recycle delay of 0.5 set and four signal averages. The probe and sample were maintained at 297 K. The projection image is the NMR equivalent of a transmission light micrograph where the image represents the NMR signal integrated over a line of constant y. In the NMR image the axis of the Nitella is rotated 90” compared with the Iight micrograph, and the length scale is approximately identical. The cell is observed to be dividing and is sending out filamentous extensions typical of Chlorophyta cell division. The cell walls are clearly visualized as regions of decreased intensity, and as before a perimembrane signal enhancement is seen. After the probe was cooled to 213 K, the NMR image on the right of Fig. 5B was obtained under otherwise identical conditions. Though the SNR was modestly improved, considerable blurring is noted due to mechanical motion of the sample coil in the rapid warm nitrogen gas stream within the sample area required to maintain the sample at room temperature. This technical problem will be addressed in future work. DISCUSSION Historically, statements of limits on NMR imaging have proved to be shortsighted. Proton imaging of the human body in fields over 0.3 T was predicted early on to be impossible.tg SNR will ultimately limit spatial resolution in NMR microscopy, and the trends noted
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Fig. 4. Microscopic images of a single green alga cell (Micrasterias). (A) A light micrograph with a scale demonstrating the contour of the spiny disk-shaped cell wall. A complete 3D NMR image data set was then obtained using a spin-echo sequence with 16 signal averages. The echo time
was 8 msec and TR was 400 msec; 64 and 32 y- and z-phase encoding steps were used respectively. (B) A 12-pm slice from the 3D data set at approximately twice the scale of the light micrograph. The oval ring of decreased signal intensity corresponds to the cell wall. The intensity of the image from the central region of the cell, which contains the nucleus, chloroplasts, and other organelles, is greatly reduced in this Lrrweighted image.
in Table 1 provide a useful guide for practical expectations. One cannot expect the same high-quality images seen in MRI of human brains to be produced from single cells. Improved filling factor and probe noise reduction are the most apparent means for improving SNR. Our studies indicate that the most significant gains in SNR can be obtained by maximizing the inductive coupling of the sample to the probe. Practically, the manufacturing of microcoils poses major challenges,
with significant room for improvement. One must be careful in choosing the material for the microcoils to avoid susceptibility artifacts. We have noted large artifacts on several occasions from localized impurities in the coil wire. Additionally, attention must be given to the reduced surface area and requisite increase in resistance of such coils. There have been reports of efforts to use high-temperature superconducting materials for probe conductors in medical MRI coils. The theoretical justification for this is given by Eq. (3),
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ulOOpm (4
(B) Fig. 5. Microscopic projection images of the dividing green alga Nitella. (A) A light micrograph demonstrating the budding of progency cells from the main cell stem. (B) An NMR projection image of the same cell cluster obtained (left) using only the x and z gradients with the probe maintained at 297 K. The budding extensions of the dividing cell are clearly visualized as in the light micrograph (note that the sample axis was rotated 900). The probe assembly was cooled to 223 K and an NMR image obtained under otherwise identical conditions (right). Though the SNR improved modestly, the physical motion of the sample due to the high gas flow rate required to keep the sample at 297 K caused a reduction in resolution.
whereby an increase in SNR by the square root of the coil resistance is noted. Note that this improvement will be realized even in the presence of the significant coil loading by the patient [( QU/QL), = ( Qu/QL)2 = 101. Probe cooling offers an additional means of improving SNR in NMR microscopy. Our data is consistent with the theoretical predictions over a relatively small temperature range; however, we would expect the agreement to continue to significantly lower temperatures. Major technical and design problems such as mechanical stability, which limited the spatial res-
olution in our microscopic images of cells using the cooled assembly, have yet to be overcome. Improved cryogenic and thermal design is also needed to allow further reduction in circuit temperature while maintaining the appropriate sample temperature environment. Though the fundamental limit is SNR, the major practical hurdles to reliable NMR microscopy are (1) mechanical motion of the apparatus, (2) instrument stability, and (3) sample viability. These factors will prevent indefinite signal averaging and need to be seriously considered in the engineering design of microscopic imaging systems.
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Acknowledgmenfs-The authors acknowledge and thank the scientific staff of the Comprehensive NMR Facility (supported by NIH Grant RRO0995) at the Francis Bitter National Magnet Laboratory, Cambridge, MA, for their technical support. Also, D.J. Ruben and J.W. Wrenn provided extensive technical support and many helpful discussions. A. Tannus and L.J. Neuringer’s reviews of the manuscript were greatly appreciated. This work was supported in part by the Whitaker Health Sciences Fund and an NSF PYI award (DIR-9057151). REFERENCES 1. Mansfield, P.; Grannel, P.K. “Diffraction” and microscopy in solids and liquids by NMR. Phys. Rev. B. 12:
9:3618-3634; 1975. 2. Hinshaw, W.S. Image formation
3. 4.
5.
6.
7.
8.
9.
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