optimizing the intrinsic signal-to-noise ratio of mri strip detectors

Optimizing the Intrinsic Signal-to-Noise Ratio of MRIStrip Detectors

Ananda Kumar1,2 and Paul A. Bottomley1,2*

An MRI detector is formed from a conducting strip separated bya dielectric substrate from a ground plane, and tuned to aquarter-wavelength. By distributing discrete tuning elementsalong the strip, the geometric design may be adjusted to opti-mize the signal-to-noise ratio (SNR) for a given application.Here a numerical electromagnetic (EM) method of moments(MoM) is applied to determine the length, width, substratethickness, dielectric constant, and number of tuning elementsthat yield the best intrinsic SNR (ISNR) of the strip detector at1.5 Tesla. The central question of how strip performance com-pares with that of a conventional optimized loop coil is alsoaddressed. The numerical method is validated against theknown ISNR performance of loop coils, and its ability to predictthe tuning capacitances and performance of seven experimen-tal strip detectors of varying length, width, substrate thickness,and dielectric constant. We find that strip detectors with low-dielectric constant, moderately thin-substrate, and lengthabout 1.3 (�0.2) times the depth of interest perform best. TheISNR of strips is comparable to that of loops (i.e., higher closeto the detector but lower at depth). The SNR improves with twoinherently-decoupled strips, whose sensitivity profile is well-suited to parallel MRI. The findings are summarized as design“rules of thumb.” Magn Reson Med 56:157–166, 2006. © 2006Wiley-Liss, Inc.

Key words: MRI coils; detectors; optimization; signal-to-noiseratio; phased-array

The planar strip array (PSA) is a phased-array detector thatwas recently introduced for conventional and parallel spa-tially-encoded MRI (1). Instead of an array of conventionalloop coils, the PSA consists of parallel conducting stripsthat are covered and separated from a virtual conductingground plane by a low-loss dielectric substrate. Each stripserves as an individual detector and is connected to itsown preamplifier. The strips are tuned by adjusting theirlengths, L, and separation, h, from the ground plane to �/4,�/2, or multiples thereof, where � is the electromagnetic(EM) wavelength at the MRI frequency. The original PSAexhibits important advantages over conventional loop-coilphased arrays. The mutual coupling between detectors isessentially eliminated (1), and the self-resonance frequen-cies of strips are intrinsically higher than loop detectors

and can potentially outperform loops at frequencies atwhich loops are no longer tunable. This suits the PSA wellfor large arrays, massively parallel MRI, and high-fre-quency MRI (2).

Because of the limited ability to adjust the substrate’sdielectric properties in the original PSA, strip length iseffectively fixed by tuning, and is therefore not a designparameter that can be flexibly adjusted to optimize thesignal-to-noise ratio (SNR) performance for specific appli-cations. Accordingly, n distributed lumped tuning ele-ments were introduced to permit the �/4 or �/2 conditionsto be met with strip lengths that can be selected based onthe performance requirements of the specific application(3,4). This leaves two questions for this technology that arecentral to its utility: what is the optimum geometry for thestrip, and how does an optimum strip perform relative toan optimum loop?

Loop surface coil detectors were adopted in the early1980s for MRI (5,6) from prior uses in NMR (7). The in-trinsic SNR (ISNR), which is defined as the SNR that adetector can achieve if the detector and MRI system lossesare excluded (8), measures the potential SNR performanceof a particular detector geometry and therefore permitsperformance comparisons of different detector geometries.For example, in the quasistatic field limit, the geometry ofthe loop detector that produces the maximum ISNR hasbeen determined both numerically (9), and analytically(10). Thus, for a region of interest (ROI) lying at depth d ina semi-infinite planar sample, the loop geometry deliver-ing the maximum ISNR has radius

a � d/�5. [1]

This relationship is central to optimizing SNR gains fromhead and body phased-arrays fabricated from individualloop coil elements (11). However, a comparable expressionfor the single tuned strip detector element of a tunable PSAdoes not yet exist. Conceivably, the optimum strip geom-etry is a function of the substrate dielectric constant, �r; thedielectric thickness or strip spacing from the groundplane, h; strip width, W; the number of lumped tuningelements, n; and the strip length, L.

To address the core question of the SNR performance ofthe strip detector and its optimum design, we numericallyanalyzed the dependence of the ISNR of a single stripelement on the parameters L, h, W, �r, and n. Using thereciprocity principle, the ISNR is calculated for a tunedstrip loaded with a homogeneous sample that has EMproperties similar to those of the human body. The electricand magnetic fields are computed by solving the mixedpotential integral (MPI) field equations employing themethod of moments (MoM), which has been widely ap-plied to compute the fields in objects whose size is com-

1Division of MR Research, Department of Radiology, Johns Hopkins Univer-sity, Baltimore, Maryland, USA.2Department of Electrical and Computer Engineering, Johns Hopkins Univer-sity, Baltimore, Maryland, USA.Grant sponsor: NIH, National Center for Research Resources; Grant number:R01 RR15396.*Correspondence to: Paul A. Bottomley, Johns Hopkins University, Depart-ment of Radiology, JHOC4221, 601 N. Caroline St., Baltimore, MD 21287-0843. E-mail: [email protected] 18 August 2005; revised 17 February 2006; accepted 28 February2006.DOI 10.1002/mrm.20915Published online 24 May 2006 in Wiley InterScience (www.interscience.wiley.com).

Magnetic Resonance in Medicine 56:157–166 (2006)

© 2006 Wiley-Liss, Inc. 157

parable to or smaller than the wavelength (12–14). Com-putations are iterated over a practical range of design pa-rameters to derive a “recipe” that optimizes the strip’sISNR performance at a given sample depth. Several MRIstrip detectors are fabricated and their ISNR performanceis measured to test the validity of the numerical simula-tions. Finally, the SNR performance of the optimized stripand a pair of strips is compared with that of a conventionalloop both experimentally and theoretically.

MATERIALS AND METHODS

Numerical Analysis

The voltage ISNR in MRI can be written as (10):

ISNR �Vsig

Vnoise�

�0�VM0�Bt��4kT�fRL

, [2]

where Vsig and Vnoise are the peak signal amplitude perunit noise and the rms noise voltages, respectively, in unitbandwidth, �0 is the Larmor frequency in rad/sec; �V isthe voxel volume; M0 is the magnetization; Bt is the rotat-ing component of the transverse RF magnetic field pro-duced by the strip with one ampere of current at theterminals; k is Boltzmann’s constant; T is the absolutetemperature; �f is the receiver bandwidth (the bandwidthof the anti-aliasing filter used for acquiring the MRI signal);and RL is the noise resistance of the sample-loaded detec-tor. Thus, ISNR is proportional to the ratio Bt/�RL (15,16).In an ideal detector in which the coil losses are negligiblecompared to those in the sample, the noise resistance RL isproportional to the power loss in the sample volume (17).In this case,

RL � �V

��E� �2 dV [3]

where � is the conductivity of the sample medium, E� is theelectric field intensity in the sample volume, and the sum-mation is defined over the entire sample volume.

MoM

Numerical analysis was performed with FEKO solver (EMSoftware and Systems, South Africa) software employingspecial Green’s function techniques for multilayer sub-strates (12). Candidate conducting strips are subdividedinto NJ triangular patches for the MoM formulation assum-ing a uniform surface current density (J�s) distribution ineach triangular patch, with EM fields resulting from theimpressed voltage source denoted as E� and H� . For a per-fectly conducting strip, the electric field integral equation(EFIE) is based on superposition of impressed (subscript i)and scattered (subscript s), E-fields. In the plane of thestrip:

E� strip � E� s � E� i � 0 [4]

Triangular meshing on strips for electric surface currentdensity (J�s) uses Rao-Wilton-Glisson basis functions(18,19) with expansion coefficients �n:

J�s � �n�1

NJ

�n � f�n [5]

where NJ represents the number of triangular patches.Similarly, metallic wires that connect the capacitors toground are discretized into electrically small wire seg-ments. Overlapping triangular basis functions gn are usedto model the line current I along these wire segments withexpansion coefficients n, such that:

I � �n�1

NI

n � gn [6]

where NI represents the number of wire segments.The EFIE expressed in compact form in Eq. [4] is solved

using the MoM as a Galerkin method (14) in which theexpansion and testing functions are considered as bothsurface patches (Eq. [5]) and wire attachments (Eq. [6]).The currents are solved from a linear combination of N �NJ NI expansion functions in a system of linear equa-tions. After the current distribution is determined, theimpedance and power losses are calculated. The net mag-netic field at each point in space is the phasor sum of thefield produced at that point by the current in each meshelement. Computation of its transverse component dividedby the square root of the power loss with one amperecurrent at the excitation source then yields a measure thatis directly proportional to ISNR (16).

For the EM simulations, candidate conducting strips arefirst numerically tuned to �/4 at an MRI frequency of63.87 MHz (1.5 T). Resonance is achieved by terminatingone end to the ground plane while maximizing the inputimpedance at the feed point. The magnitude of Bt is cal-culated as one-half of the root of the sum of the squares ofthe net transverse field components generated by the unitcurrent applied at the feed point, with strips orientedparallel to the z-axis of the main magnetic field. The noiseresistance, RL, in Eq. [3] could be calculated by integratingthe E-field over the entire sample volume. However, RL ismore efficiently determined from the input impedance ofthe strip with one ampere source (16). Because it yieldscomparable results about 100 times faster in our imple-mentation, we use that approach.

We consider �/4 wavelength strip detectors, each em-bedded in a dielectric material of �r � �r

substrate, with oneend connected to a unit current excitation source that isperfectly matched to the strip impedance, and the otherend terminated to the conducting ground plane as de-picted in Fig. 1. In all cases both the dielectric and theheight between the strip and ground (h), and that betweenthe strip and the upper dielectric layer (g), is the same (h �g) except when an air dielectric (�r � 1) is used. The losstangent, tan � was assumed to be 0.001, which is typical ofdielectric substrates and corresponds to negligible conduc-tivity at RF frequencies. In the case of an air dielectricbetween the strip and ground plane, the gap g included the

158 Kumar and Bottomley

height h plus a 3-mm-thick acrylic sheet (�r � 2.6) toprovide mechanical support and insulate the sample fromthe conductor. For the numerical calculations we assume asample comprised of a homogeneous semi-infinite plane ofmuscle tissue with dielectric constant �r

sample � 77 andconductivity � � 0.34 S/m at 63.9 MHz, as measuredpreviously (20), laid on top of the detector. We assume thatthe ground plane is perfectly conducting and that both theground plane and the strip have infinitesimal thickness.The cable feed point is modeled as a uniform verticalcurrent segment of length h. Surface currents are inducedon the topside of the ground plane, on both sides of themetallic strip, and on the wire segments connecting thelumped capacitors to the ground plane (19). To determinethe surface currents on the strip, the strip is divided intotriangular patches with sides of length � � 0.01�f, where �f

is the free-space wavelength at the MRI frequency. Allcalculations are performed on an Intel P4 personal com-puter (2 GHz CPU, 512 MB RAM) with 72 (L � 10 cm, W �6 mm) to 512 (L � 20 cm, W � 25 mm) triangular elementsin the strip. Bt is calculated over a selected plane or a pointin the sample.

Numerical Validation

The numerical method is tested by applying it to calculatethe ISNR of loop coils of radii from 10 to 70 mm, andcomparing the results with the known analytical behavior(10) computed from Eqs. [1] and [2]. The ISNR for eachloop measured at its optimum depth is plotted as a func-tion of the radius in Fig. 2. The overlap of the curves overseveral orders of magnitude of the ISNR engenders confi-dence that our numerical analysis technique of 1) tuningeach detector, 2) calculating its Bt, and 3) determining RL

from the power losses yields, in toto, results that are inagreement with prior analytic findings for the loop. Thenumerically calculated ISNR at 100-mm depth is also plot-ted as a function of coil radius in Fig. 2, demonstrating thatISNR is indeed maximum for a 45-mm radius loop, aspredicted by Eq. [1] (9,10).

Numerical Optimization

To determine the strip design parameters that yield theoptimum ISNR, rigorous numerical MoM ISNR calcula-tions are performed for a large number of individual stripsincorporating a wide range of the five design parameters(W, h, �r

substrate, n, and L). After each strip is tuned, ISNRdata for each strip are computed over a two-dimensional(2D) section that lies perpendicular to the ground-planeand intersects the long axis of the center of the strip.Signals at representative points at z � 0.75 L that liedirectly above the center of the strips are selected forcomparison. To condense the number of variables beingsimultaneously optimized, the ratio W/h is substituted forW with h � 5 mm, 10 mm, and 15 mm. The ISNR depen-dence on �r

substrate is computed over the range of 1–10, andL is varied from 50 mm to 300 mm.

The ISNR of numerically-optimized strip detectors thatresult from the above procedure are then compared di-rectly with the numerical ISNR of single loop coils com-puted using identical sampling properties. In addition, to

FIG. 2. The ISNR (arbitrary units, log scale) of loop coils of radii �10–70 mm at their optimum depths relative to the conductor at y �0, calculated on the axis numerically (squares), and using the ana-lytical solution (Eq. [1]; triangles, overlapping), as a function of coilradius (top curves). The analytical values were normalized to thesingle numerical value of the ISNR at an optimal depth of 22 mm fora 20-mm radius loop. The numerical ISNR at a fixed depth d�100 mm is also plotted as a function of coil radius in the solidcurve (crosses, bottom). This curve shows that a 45-mm radius coilproduces the maximum ISNR at a depth of 100 mm, as expectedfrom the analytical expression for optimal loop (Eq. [1]).

FIG. 1. a: Diagram showing parameters for a tuned �/4 strip detec-tor of length L with three lumped capacitors. The cross-sectionalview (bottom) shows the strip, dielectric material and acrylic sup-port, lumped capacitor, and ground plane. The strip of width W isseparated from the ground plane by dielectric material thickness h,and from the surface by a dielectric overlay of thickness g. The feedpoint is connected to a perfectly matched excitation source fornumerical simulations, and directly to a matching circuit duringexperiments. b: Photograph of a single 20-cm strip detector ele-ment with coaxial cable attached for impedance measurement.

Optimizing MRI Strip Detectors 159

permit absolute comparisons of numerical ISNR and theexperimental ISNR of loops and strips, numerical ISNR isconverted to absolute values in ml–1 Hz1/2 using Eq. [2]and M0 � 0.00326 Am–1T–1 for water (10), with values ofT, �f, and �V corresponding to the experiment. Recogniz-ing that a section through a loop intersects two (un-grounded) conductors compared to the single conductor ofa strip detector, a two-strip detector may arguably providea fairer ISNR comparison with the loop. Therefore, theSNR performance for the loop is also compared experi-mentally with that of a detector comprised of two paralleloptimized strips.

Experimental Validation

To test the findings of the numerical analysis, seven single-strip detectors tuned to �/4 at 63.87 MHz with L � 10 cm(W/h � 1), 15 cm (W/h � 1; using air with �r

substrate � 1 andepoxy glass with �r

substrate � 5 ), 20 cm (W/h � 1, 2, and 4;air dielectric), and 30 cm (W/h � 1; air dielectric) werefabricated. A copper-clad printed circuit board is used as aground plane with copper tape (3M Corp., MN, USA) forthe strips. Ceramic chip capacitors (American TechnicalCeramics Inc., CA, USA) serve as lumped elements to tunethe detectors. The conducting strip and acrylic sheet indetectors employing air dielectrics are supported withacrylic rods. The two-strip detector for the loop coil com-parison is fabricated with L � 20 cm strips and h � 6 mm,separated by 5 cm in an air gap (�r

substrate � 1). All strips areaccurately tuned and matched (reflection coefficient, �0.1) to a 50 � coaxial cable connected to the scannerreceiver chain via the high-quality factor (Q) capacitor/inductor matching circuit illustrated in Fig. 3. To test thenumerical tuning algorithm, the experimentally-deter-mined tuning capacitances are compared with the numer-ically-determined values.

The ISNR performance of strip detectors is comparedwith commercial GE Medical Systems (Milwaukee, WI,USA) loop coils of diameter 14 cm (5.5 inches) and 7.6 cm(3 inches). The pixel and system SNR, as well as the ISNRperformance (8), are measured for each detector loadedwith a 20-L cubic phantom of CuSO4-doped 0.35% NaCl

solution. Experiments are performed with a GE 1.5T CV/iMRI scanner employing a gradient refocused echo (GRE)pulse sequence (TR � 100 ms, TE � 3.2 ms, NEX � 2; flipangle � 90°; slice thickness � 10 mm). The image (pixel)SNR is derived from the ratio of the signal level at a givendepth d to the offset-corrected root mean square (rms) ofthe background noise in the same image. The system noisefigure for the scanner is measured from the ratio of the rmsnoise of a 50 � resistor recorded at ambient and liquidnitrogen temperatures while it is connected to the pream-plifier and scanner (21). With TE �� T2 and TR �� T1 forthe phantom, the system and ISNR did not require correc-tion for relaxation effects. The loaded and unloaded Qs forthe ISNR calculations (8) are measured on a Hewlett Pack-ard HP 23605 network analyzer equipped with an imped-ance test module.

RESULTS

A computed 2D plot of the ISNR of a single �/4 stripdetector with L � 100 mm, �r � 1, h � 6 mm, W � 6 mm,tuned with n � three 68.4pF capacitors is shown in Fig. 4.Note the sensitivity gradient from end to end, which isintrinsic to the original �/4 design (1). In practice, theranges of W, h, �r, n, and L that can be evaluated are limitedby the practical constraint that strips must be tuned. As Lis increased, for example, the net capacitance needed totune a strip is increasingly dominated by the strip induc-tance and substrate capacitance, which reduces the effectof the lumped elements (Table 1). Eventually the distrib-uted substrate capacitance becomes so large that stripscannot be effectively tuned with additional lumped capac-itors.

ISNR Dependence on Dielectric Constant

The calculated ISNR as a function of W/h with h � 5 mmat a depth of 50 mm is plotted in Fig. 5a for three stripswith L � 150 mm and substrate dielectric constants of 1, 2,and 5. The corresponding ISNRs as a function of depth forthe 150 mm strip made with epoxy glass (�r

substrate � 5) andair (�r

substrate � 1) are shown in Fig. 5b. The calculatedISNR is nearly 50% lower with the epoxy glass substratecompared to the air dielectric. This result is essentiallyindependent of W/h. The numerical analysis supports afinding that ISNR decreases as �r

substrate increases aboveunity for the range 1 � �r

substrate � 10 investigated. Thisnumerical finding is not due to losses in the dielectric perse, because neither a 10-fold increase nor a 10-fold reduc-tion in the dielectric loss tangent significantly affects thecalculated ISNR values. It appears that as �r

substrate de-creases, the magnetic field (signal) in the sample increasesfaster than the square root of the noise. The detrimentaleffect of higher �r

substrate on antenna efficiency is attribut-able to other loss mechanisms to which the MoM full-waveanalysis is sensitive (22). As usual, air (or vacuum) is best!

This finding is consistent with the experimental pixelSNR data from the �r

substrate � 1 and �rsubstrate � 5, 150-mm-

long strips, whose SNR curves are also plotted in Fig. 5band overlap the calculated curves.

ISNR and the Number of Tuning Capacitors

Provided that the strips are tuned to �/4, increasing thenumber of capacitors from one (located at the strip center)

FIG. 3. Schematic diagram showing the high Q matching circuit forstrip detectors. C1, L1, C3 are impedance matching elements; C2 isa DC blocking capacitor; and L2 and the pin diode D function asdecoupling elements. The ranges of values used for our experimen-tal strip detectors were as follows: C1, 25–30 pF; C2 � 1000 pF; C3,120–200 pF; L1, 250–300 nH; and L2, 20–40 nH. A 50-Ohm coaxialcable is attached at RF out.


to 10 (equally-spaced) did not significantly affect the stripISNR. In contrast to loops, in which capacitance increasesas the number of distributed elements increases, the ca-pacitance values needed to tune strips to �/4,decreasesboth as the number of capacitors increases and the striplength increases, to counteract the increasing contributionfrom the dielectric substrate. Table 1 compares the exper-imentally determined capacitor values needed to tune thestrips with capacitance values computed using 72–512triangular surface patches in the MoM formulation. Theexcellent agreement between calculated and experimentaltuning capacitances is within the accrued 5% tolerances ofthe chip capacitors used, and validates the practical per-formance of the numerical tuning algorithm.

ISNR Dependence on W/h, h, and W

In Fig. 6a the computed ISNR of a strip of L � 100 mm withair dielectric (�r

substrate � 1 plus an acrylic sheet) is plotted

FIG. 5. a: ISNR (same units as in Fig. 2) for h � 5 mm, L � 150 mmstrip detectors calculated at (x, y, z) � (0, 50 mm, 100 mm) as afunction of W/h for three dielectric substrates with �r � 1, 2, 5 aslabeled. SNR is higher with air dielectric compared to an all-acrylic(�r � 2) and epoxy glass (printed circuit board substrate, FR4 with �r

� 5) substrates, and declines slowly with W/h ratio. b: Experimentaland numerical SNRs plotted as a function of depth for two h �5 mm, L � 150 mm strips fabricated from substrates with �r � 1 (air)and �r � 5 (epoxy glass), as annotated. The numerical curves arenormalized to the (single) peak value of the experimental curve.

FIG. 4. a: Numerical ISNR (linear scale at bottom,same units as in Fig. 2) profile of an L � 200 mmstrip with W/h � 25/6, �r

substrate � 1 and n � 3,calculated along the length of the strip (horizontalz-axis) in the yz plane with y � 0 at the top surface.The sensitivity gradient follows the typical �/4wavelength pattern. b: Current density distributionalong the strip length on the triangular surfaces ofthe 200 mm strip in a, depicting the 536 triangularpatches. Logarithmic surface current density from2 A/m (light blue) to 4 A/m (red).

Table 1Comparison of Numerically- and Empirically-Determined TuningCapacitors

DetectorExperimental

capacitorvalue (pF)

Numericalcalculationcapacitorvalue (pF)

L � 10 cm; W/h � 1; �r � 1 68 68.5L � 15 cm; W/h � 1; �r � 1 51 50L � 15 cm; W/h � 1; �r � 5 52 51L � 20 cm; W/h � 1; �r � 1 43 41L � 20 cm; W/h � 2; �r � 1 51 52L � 20 cm; W/h � 4; �r � 1 62 67L � 30 cm; W/h � 1; �r � 1 24 28


as a function of W/h at depths of 30 mm, 50 mm, and100 mm, with three different values of h (5 mm, 10 mm,and 20 mm). As shown in Fig. 5a, the ISNR declines slowlywith W/h �1 for h � 5 mm. However, here we see thatISNR declines more severely as h increases, albeit only atshallow depths. For example, at 100 mm depth, the de-crease in ISNR is �5% over the range of 0.5 � W/h � 5 forall strips with lengths of 50 mm � L � 300 mm. Note thatbecause detectors are designed with equally thick layers ofdielectric above and below the conductor, and depth ismeasured from the top of the detector, the distance be-tween the conducting strip and the sample increases withh. This raises the question of whether the ISNR reductionwith h is due to the increased distance between the stripand sample. The effect on ISNR of removing the upperdielectric layer entirely, except for the 3-mm acrylic sheetthat is used for mechanical support and/or electrical insu-lation, is shown in Fig. 6b at a fixed depth above theacrylic, for air and epoxy-glass substrates. Removing theupper dielectric layer (including air dielectric) reducesISNR despite the reduction in distance between sampleand strip. Thus, the inclusion of the upper dielectric isimportant for strip performance and is not responsible forthe ISNR decline with h.

Experimental data from L � 200 mm strips preparedwith air gaps of h � 6 and 20 mm, and widths of W � 6, 12,and 25 mm are presented in Fig. 7. These data are essen-tially consistent with the numerical findings of Fig. 6.Figure 7a, with fixed h � 6 mm, shows some advantage fornarrow strips at shallow depths (� 20 mm). Wider stripsare better at depths above 30 mm, offer the added benefit of

a wider FOV in the transverse (xy) plane for 1 � W/h � 4.The notion that the ISNR declines for larger air gaps isconfirmed experimentally by data from two strips with h �6 mm and h � 20 mm, as shown in Fig. 7b. The ISNR of theh � 20 mm strip decreases to 30–50% at depths d �50 mm due to the 3.3-fold increase in substrate thickness.The experimental data derive from W � 25 mm, L �200 mm strips whose measured unloaded Q-values de-crease from 183 to 120 as the substrate thickness is in-creased.

ISNR Dependence on L

Figure 8 shows the variation of the computed ISNR alongthe z-axis for strips of various lengths from 50 to 300 mmdesigned with the parameters that yield the best practicalperformance as determined above (air dielectric withacrylic support sheet, W/h � 1, and h � 6 mm). Theintrinsically nonuniform, almost sinusoidal ISNR profilealong the �/4 strip length noted for Fig. 4 is apparent for all

FIG. 7. a: Experimentally measured ISNR for L � 200 mm, h �6 mm, and �r � 1 strips, as a function of depth for W � 6, 12, and25 mm. Wider strips show some ISNR improvement at depthsabove 30 mm. b: Experimental and numerically determined ISNRsfor two L � 200 mm, W � 25 mm, and �r � 1 strips fabricated withsubstrate thicknesses, h � 6 mm and 20 mm. The numerical curvesare normalized to the (single) peak value of the experimental curve.SNR declines as the air-gap, h, increases.

FIG. 6. a: Numerical ISNR (same units as in Fig. 2) as a function ofW/h for h � 5 mm (triangles), 10 mm (gray squares), and 20 mm(circles) at depths y � 30 mm, 50 mm, and 100 mm for L � 100 mmstrips. ISNR is reduced as h increases at lower depths. b: NumericalISNR as a function of h at a depth d � 30 mm above the topsurfaces of detectors with �r � 1 (triangles) and �r � 5 (squares)dielectrics with (filled symbols) and without (empty symbols) theupper dielectric layer (L � 200 mm, W � 10 mm).


strip lengths, with maximum values achieved at z � 0.7 L.Note that although longer strips exhibit broader regions ofhigh ISNR than shorter strips along their axes, the unifor-mity of the shorter strips along their full length is better.Figure 8a also demonstrates that the ISNR at a given depthd is a slow function of L, varying by only 2% over the ranged � L � 3d/2 at d � 100 mm in this example. To obtain anempirical expression for the strip length that yields theoptimum ISNR at a given sample depth d analogous to Eq.[1] for loops, the analysis of Fig. 8a was repeated for manystrip lengths 50 mm � L � 300 mm and depths 50 mm �d � 200 mm. Figure 8b is a scatter plot of those striplengths that yield ISNR values which are within 2% of themaximum ISNR determined at each of the depths plottedon the horizontal axis. The slope of the line of best fityields the expression L � 1.3 (�0.2) d for the strip lengththat yields the optimum ISNR at an imaging depth d for therange investigated.

ISNR of Experimental Strip and Loop Detectors

Table 2 lists the experimental ISNR (upper figures) andraw pixel SNR (lower figures) measurements at the set ofdepths comprised of the optimum depths for each of thestrips and loops investigated. The ISNR of each detectormeasured at its putative optimal depth (d � L/1.3 for astrip detector, d � �5a for a loop coil) are located in theshaded boxes. Note that the ISNR of the 5.5-inch loop coilunderperforms many strips, even though the ratio of itsunloaded to loaded Q is very high. Except for the 200-mmstrip, the pixel SNRs of the strips that we built generallyunderperform those of both of the loops to a greater extentthan does the ISNR, due to the lower loading factors (QU/QL) for the strips.

Figure 9 compares the absolute numerical and experi-mental ISNR performance of the 3-inch (a � 38 mm) GEloop surface coil, which should perform optimally for d �

FIG. 8. a: Numerical ISNR (same units as in Fig. 2) profile along thez-axis at 100-mm depth for a range of strips of length 50 mm � L �

300 mm (legend at right) oriented along the z-axis, all with airdielectric, acrylic support sheet, W/h � 1, and h � 6 mm. Peak SNRfor each strip occurs at about z � 0.75 L along the nonuniformprofiles, but peak SNR is a relatively slow function of L. b: Scatterplot of strip lengths that produce an SNR that lies within 2% of themaximum ISNR for a given depth (horizontal axis) in the range of50 mm � d � 200 mm. The strips use air dielectrics with acrylicsupport, W/h � 1, and h � 6 mm. The gradient of the curve of bestfit gives the relation between the optimum strip length for a givendepth, L � 1.3(�0.2)d for these detectors.

Table 2Intrinsic SNR (ml�1 Hz1/2, Upper Figures, Bold Type) and Raw Pixel SNR (Lower Figures) for All Experimental Loop and Strip DetectorsMeasured at the Set of Depths That Correspond to the Optimum Theoretical (Intrinsic) SNR for All of the Strips and Loops Investigatedin This Study*

DetectorQ factor Depth (mm)

QU QL 77 85 115 155 230

3-inch GE loop 179 44 5700 4652 2485 1130 336189 154 82 37 11

5.5-inch GE loop 260 20 3337 2686 2084 875 77122 98 76 32 3

L � 10 cm; W/h � 1; h � 6 mm; �r � 1 139 122 5701 4685 2285 1078 63776 63 30 14 8

L � 15 cm; W/h � 1; h � 6 mm; �r � 1 128 93 3443 2727 1344 623 32067 54 27 13 6

L � 15 cm; W/h � 1; h � 6 mm; �r � 5 75 61 2382 1843 965 561 31439 30 16 9 5

L � 20 cm; W/h � 1; h � 6 mm; �r � 1 189 126 3774 2864 1568 981 44283 63 34 22 10

L � 20 cm; W/h � 4; h � 6 mm; �r � 1 183 84 4685 3929 2274 994 410131 110 64 28 11

L � 30 cm; W/h � 1; h � 6 mm; �r � 1 220 148 3211 2706 1509 734 41670 59 33 16 9

*The depth corresponding to the theoretical optimum for each detector is shaded. QL and QU are the loaded and unloaded coil qualityfactors.


85 mm based on Eq. [1], and a L � 200 mm strip withW/h � 4, h � 5 mm air gap, and 3-mm acrylic sheet. Theloop has eight equally-spaced tuning capacitors aroundthe circumference that were included in the analysis. Thecurves show essential agreement between the absolute nu-merical ISNR calculations and experiment, with devia-tions generally � 10% (see inset). At depths d � 20 mmclose to the sample, the discrepancy between numericaland experimental curves is greater for the loop (� 15%).

Nevertheless, both the numerical and experimental mea-surements show that the ISNR of the strip is up to doublethat of the loop. At greater imaging depths, the 3-inch GEloop outperforms the strip, with a maximum of �20%better performance at the loop’s optimum depth (see in-set).

Loop vs. a Two-Strip Detector

To improve the depth of signal detection for the strip, twostrips were combined in parallel. Figure 10a and b com-pare the experimental sagittal (zy-plane) raw pixel SNRprofiles of the 3-inch (a � 38 mm) loop detector and atwo-strip detector fabricated with L � 20 cm, h � 6 mm, s� 5 cm separation and air dielectric. In Fig. 10b the imageplane bisects the space between the two strips, whereinthe two-strip detector exhibits a �15 % improvement inpixel SNR compared to that in the equivalent sagittal planeoffset 2.5 cm from a single 20-cm strip (annotated in Fig.10d). The coupling between the two strips was measuredat –26 dB, which agrees with the numerically computedvalue of –27 dB. The pixel SNR profiles of the loop and thetwo-strip detector in Fig. 10a and b are comparable: theparallel strips have a more extended SNR profile than theloop, but the maximum pixel SNR is a little higher for theloop. A sagittal image from the spine of a normal volunteerobtained with the two-strip detector is shown in Fig. 10c.Figure 10d shows the sinusoidal-like sensitivity of thetwo-strip detector in the transverse (xy) plane. Note thatthe sensitivity of the two-strip array is actually higher thanthe center plane depicted in Fig. 10b, immediately aboveeach strip.

The results of the numerical and experimental analysisare summarized as “rules of thumb” for designing stripdetectors that maximize ISNR in Table 3.

FIG. 9. Absolute numerically-determined (num), and experimental-ly-measured (exp) ISNRs as a function of depth compared for a strip(L � 200 mm; W/h � 4; �r � 1 with acrylic support) at z � 0.75 L, andon the axis of a 3-inch (a � 38 mm radius) loop coil with eightdistributed tuning capacitors. Inset shows the region 30–100 mmdeep with vertical scale doubled.

FIG. 10. a: Experimental sagittal (yz-plane at x � 0) pixel SNR (signal/rms noise, not ISNR) of the GE 3-inch (a � 38 mm) loop coil and a20-L water phantom. b: Experimental sagittal SNR profile in the middle (X � 0 plane) of two L � 20 cm, h � 6 mm strip detectors that arespaced 5 cm apart at X � �2.5 cm on the same 20-L water phantom. Color contour intervals are at pixel SNR values of 500, 200, 100, 50,30, and 10. c: Example of sagittal fast spin-echo (FSE) image of the spine of a healthy volunteer produced by the two-detector array (TR �4000 ms, TE � 72 ms, NEX � 2, slice thickness � 4 mm, FOV � 28 � 28 cm, 256 � 192 points). d: Axial fast gradient-echo image of thewater phantom (TR � 100 ms, TE � 3.2 ms, NEX �2, slice thickness � 4 mm, FOV � 28 � 28 cm, 256 � 192 points). The dotted lineillustrates sinusoidal sensitivity profile for sensitivity encoding and extracting spatial image harmonics. The vertical line indicates the sagittalplane represented in part b (the SNR is higher immediately above the strips).


DISCUSSION

The MRI strip detector differs fundamentally from a con-ventional loop detector with respect to its geometry, fielddistribution, sensitivity profile, and the fact that a largerportion of its energy, if activated, may be stored as E-fieldwithin the dielectric substrate close to the strip, comparedto energy stored as B-field close to the loop. Accordingly,the strip detector exhibits spatial sensitivity and ISNRcharacteristics that are entirely different from loop detec-tors, and thus the usual design rules for optimizing loopdetectors are not applicable to strips. Here we applied“brute force” numerical analysis using the MoM to derive,for the first time, basic design rules for choosing the length,width, height, substrate dielectric constant, and number ofdistributed capacitors to optimize the ISNR performanceof the tunable strip detector for a given depth in a sample.To avoid being trapped in local optima, we spot-sampledmultiple parameters, as evident in Figs. 5a and 6, andincluded experimental checks (Table 2).

Although numerical approaches lack the elegance of ananalytic solution, it is unclear whether an analytic solu-tion can be found that incorporates all of the variablesinvestigated here. Indeed, the large number of design pa-rameters, as well as the requirement that each strip benumerically tuned, are a significant hurdle even for nu-merical approaches. In this context, note that a numericalsolution (9) also guided loop coil design before publicationof an analytical solution (10), and that even today thechoices for basic loop coil parameters, such as the numberof turns (or length), conductor size, number of distributedcapacitors, and dielectric substrate, have not been formallyoptimized as we have done here for strips. The tissueimpedance model used here was realistic for the body, asevidenced by the ability of the analysis to accurately pre-dict strip tuning capacitors and relative performance.Varying the load primarily affects the strip matching con-ditions, which do not affect the general conclusions atfield strengths for which penetration effects are not signif-icant. Although both our computed and experimental re-sults (Fig. 9, Table 2) indicate that the ISNR performanceof strips and loops are comparable at 1.5 T, ISNR perfor-

mance for strips may conceivably excel at higher MRIfrequencies where probe dimensions become comparableto EM wavelengths, and loop detectors become untunable.

Our numerical evaluations involved computing threedifferent quantities: the values of the tuning elements inthe presence of dielectric substrate and sample, the spatialdistribution of the transverse RF field, and the noise resis-tance of the entire loaded structure at resonance. We testedthe veracity of the numerical techniques, and the rules ofthumb derived therefrom, in four ways. First, we con-firmed that the numerical analysis methods correctlyyielded the established design rule for the optimum ISNRof a loop coil for a given sample depth (9,10), as prescribedby Eq. [1]. The results shown in Fig. 2 validate the calcu-lations as applied to the loop. Second, we showed thatnumerical tuning of strip detectors yielded the same val-ues within component tolerances for the tuning compo-nents that were empirically found to be necessary to tuneseven different sample-loaded experimental strip detec-tors (Table 1). Third, we directly tested the rules of thumbwith experimental SNR measurements on strip detectorsfabricated with four different lengths, two different dielec-tric substrates, two different heights, and three differentstrip widths. The analysis and experiment are in essentialagreement as substantiated by the data in Table 2, and byFigs. 5–9. The reduction in ISNR performance that resultswhen substrate thickness h is increased from 6 to 20 mm,for example, was evident in both the analysis and experi-mental data shown in Fig. 7. This behavior is consistentwith prior findings that the Q and radiation efficiency ofthe strip detector are higher with moderately thinner sub-strates (4,22). Fourth, we demonstrated agreement be-tween the numerical and experimental relative SNR per-formance of both the strip and loop detectors, as comparedone against the other (Figs. 9 and 10).

In principle, the experimental ISNR should measure thebest SNR achievable from a given detector geometry, as-suming that its losses can be made negligible compared tothe sample losses (8). Determination of the detector’sloaded and unloaded Q-factors, such as provided in Table2, are central to the calculation of ISNR from experimentalMRI data (8). Large changes in Q with loading are gener-ally, but not always (caveat), indicative of optimum detec-tor performance, even though they always result in a cal-culated ISNR that is not much higher than the measuredpixel SNR. Conversely a small decrease in Q with loadingalways results in a calculated ISNR that is much higherthan the actual (pixel) SNR. The importance of the caveatis evident in Table 2. The ISNR of the 5.5-inch loop coil atits optimum depth of 155 mm, calculated from Eq. [1], is inpractice lower than that of the 3-inch loop at the same155-mm depth. This contradicts Eq. [1], which says thatthe 5.5-inch loop should be the best. This result is ob-tained despite the fact that the large change in Q for the5.5-inch coil (from 260 to 20) might otherwise suggest thatit is a near-optimum performer. Clearly, it is not. The5.5-inch coil evidently has additional losses when loaded(likely E-field losses) for which the experimental ISNRcalculation does not properly correct. The same implica-tion might be drawn for the L � 15 cm, h � 1 cm, �r

substrate

� 1 strip. Moreover, the higher loaded Q’s, and consequentsmaller change in Q with loading, generally resulted in

Table 3Rules of Thumb for Designing �/4 Strip Detectors with OptimumISNR

I. Air dielectric (�r � 1) out-performs other dielectricsubstrates.

II. The number of tuning capacitors n � 2 does notsignificantly affect ISNR.

III. W is a weak determinant of ISNR. Increasing W, forconstant h, generally increases ISNR.

IV. ISNR decreases as h increases (h � 5 mm), forconstant W. A dielectric overlay improves ISNRperformance.

V. ISNR along the strip axis is nonuniform. The maximumis at z � 0.7L.

VI. The optimum ISNR at depth d results from a striplength L � 1.3 (� 0.2)d.

VII. The ISNR of an optimized strip detector is comparableto an optimized loop coil but is higher close to thedetector, lower at depth. The fields-of-view differ.


greater increases in the ISNR over the actual raw (pixel)SNR for strips compared to the loop coils. We do not yetknow how much the unloaded Q of strip detectors can beimproved in practice to realize pixel SNRs that are close tothe ISNR. However, the changes in unloaded Q seen inexperimental detectors used to test both the �r

substrate and hdependence in Figs. 5b and 7b were consistent with thenumerical findings for ISNR performance, which suggeststhat the effects of detector design parameters on Q are wellaccounted for by the numerical approach used here.

Importantly, our analysis and experiments show that anoptimized strip detector can provide ISNR performancecomparable to that of an optimized loop detector. Theoptimum strip has better ISNR than the optimized loopcoil close to the detector, but lower ISNR at greater depths(Fig. 9). It has a more extended sensitive volume of highISNR in the plane of the strip, but a smaller sensitivevolume perpendicular to it. These differences reflect thedifferent characteristic transverse field distributions of thestrip and loop. Putting together two optimized stripsspaced by less than the diameter of the optimum loopsubstantially improves SNR performance while it main-tains an acceptable level of decoupling between the ele-ments, an advantage of strip arrays that was underscoredin previous work (1,3). The added virtue that perpendic-ular to the strips the sensitivity profile is almost sinusoidalin nature (Fig. 10d) renders the combination of strips in anarray ideal for extracting spatial harmonics in parallelMRI.

The inclusion of lumped capacitors in the strip enablestuning over a range of strip lengths, largely eliminating theconstraint to length imposed by MRI frequency and dielec-tric substrate, and thereby permitting the geometry to beoptimized for SNR performance. Because increasing striplength and �r

substrate reduces the tuning capacitance, choos-ing the lowest possible value for �r

substrate provides themaximum range of strip lengths that can be tuned for agiven MRI frequency. Fortuitously, this minimum,�r

substrate � 1, also yields the maximum ISNR in our anal-ysis. Note also that fields propagate in strip lines in qua-sitransverse EM modes, and that optimizing the transversemagnetic field, Bt, of the strip via the geometric parameters(W, h, L, �r

substrate), is tantamount to optimizing the trans-verse magnetic (TM) mode of operation.

In conclusion, numerical MoM full-wave analysis can beused to reliably establish the tuning properties of experi-mental MRI detector coils, and to predict the ISNR perfor-mance over their tunable ranges for specific componentvalues and geometric parameters. Iterative applications ofthis analysis can be used to establish parameters that yieldoptimum or near-optimum ISNR. Thus, it transpires thatan optimized strip detector for 1.5 T has �r � 1 � W/h, adielectric overlay, and a length about 1.3 times the depthbeing imaged. The ISNR performance of an optimized stripdetector is generally comparable to, but has a characteris-tically different spatial distribution from a loop detectoroptimized for the same depth. The superior performanceclose to the strip suggests high-resolution MRI applica-

tions to the skin, spine, and cerebral cortex, and the resultsshow that multiple strips can be assembled with minimalcoupling for parallel imaging (1,4). We hope that the cur-rent work will be of value in designing and building suchdetectors.

ACKNOWLEDGMENTS

We thank Randy Giaquinto, Ronald Ouwerkerk, PeterBarker, and Leroy Blawat for valuable discussions andhelp.

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optimizing the intrinsic signal-to-noise ratio of mri strip detectors

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