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PHYS THER
Vol. 88, No. 1, January 2008, pp. 50-57
DOI: 10.2522/ptj.20060358

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Technical Reports

Variability in Effective Radiating Area at 1 MHz Affects Ultrasound Treatment Intensity

Stephen J Straub, Lennart D Johns and Samuel M Howard

SJ Straub, PhD, ATC, is Associate Professor, Department of Physical Therapy, Quinnipiac University, 275 Mt Carmel Ave FOTRN, Hamden, CT 06489 (USA)
LD Johns, PhD, ATC, is Professor, Department of Physical Therapy, Quinnipiac University
SM Howard, PhD, is Chief Technology Officer, Onda Corporation, Sunnyvale, Calif

Address all correspondence to Dr Straub at: stephen.straub{at}quinnipiac.edu


Submitted December 4, 2006; Accepted July 26, 2007


    Abstract
 
Background and Purpose: Previous research has indicated that not all ultrasound transducers heat at equal rates; however, the cause of this disparity is unclear. Variability in spatial average intensity (SAI) has been implicated in this disparity at 3 MHz. This variability has not been explored at 1 MHz.

Methods: Sixty-six 5-cm2 ultrasound transducers were purchased from 6 different manufacturers. Transducers were calibrated and assessed for effective radiating area (ERA), total output power, and SAI using standardized measurement techniques.

Results: Total output power values fell within US Food and Drug Administration guidelines, but there were large variations in ERA. The resulting SAI values showed large deviations (–43% to +61%) from the digitally displayed value. Intra-manufacturer SAI values varied up to 53%.

Discussion and Conclusion: Spatial average intensity can vary largely from the values displayed on these ultrasound generators; in a calibrated cohort, this difference is primarily attributable to differences in measured ERA. Patterns of SAI variability within the manufacturer at 1 MHz do not follow previous reports of variability at 3 MHz.


    Introduction
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Conclusion
 References
 
Therapeutic ultrasound is commonly used in the treatment of musculoskeletal injury to increase tissue temperature and increase healing rates.1,2 Unfortunately, treatment outcomes have been equivocal.3 As the practice of physical rehabilitation has matured, significant efforts have been made to establish treatment guidelines that can be linked to measurable therapeutic outcomes. As part of this drive to validate treatment protocols, a number of researchers have attempted to quantify tissue heating rates in phantom tissue,4 muscle,515 and tendon.16

Some clinicians have expressed concern that one widely referenced set of treatment guidelines for tissue heating was established using a single ultrasound head from a single manufacturer5 and questioned whether published heating guidelines could be applied universally.4,11,12 In response, studies making direct comparisons among single transducers from different ultrasound manufacturers were performed.11,12 These experiments demonstrated that individual transducers from different manufacturers may vary up to 61% in their ability to heat tissue.11,12 The authors of these studies were unable to fully explain the heating differences that they reported.

One potential factor that may account for a portion of the heating discrepancy lies in variability of the true treatment intensity.17,18 Johns et al18 have argued that the US Food and Drug Administration (FDA) guidelines,19 which permit large variability in values for total output power (in watts) and effective radiating area (ERA, in square centimeters), result in unacceptably large variability in spatial average intensity (SAI, in watts per square centimeter). The FDA guidelines19 regulate the accuracy of the output power produced, permitting a ±20% error band, and they require that manufacturers report an error band for ERA but stop short of dictating what is an acceptable percentage of error. Most manufacturers report a ±20% or 25% error for ERA; few manufacturers report an actual measured ERA value for each transducer.

In our review of how 6 manufacturers used ERA in determining SAI, 5 of the 6 tested a small sample of a larger production batch.20 If the mean value ERA of the sample falls within the error band for reported ERA, the entire batch of transducers is cleared for sale. All machine software use a standard ERA value to calculate SAI for all transducers. The combination of the reported mean ERA value, rather than the actual ERA, and the error level in output power permitted by the FDA can result in large variations in true SAI generated by the individual transducer. The FDA does not have regulatory guidelines for SAI even though most clinicians base their treatment dose on this metric.18,19 A manufacturer utilizing a combination of ±25% ERA and ±20% W permits a theoretical minimum to maximum SAI range of 150% between ultrasound heads while remaining in compliance with FDA guidelines.18

In 1982, Fyfe and Parnell17 concluded that ultrasound transducers can be operational at outputs that vary greatly from the metered value. They reported that only 5 of 18 transducers (from multiple manufacturers) met the then-current Australian Standard Specifications21 and International Electrotechnical Commission (IEC)22,23 recommended tolerance of ±15% of expected output power and only 4 of the 18 were within the tolerance level (±10%) for ERA. Pye and Milford24 tested 85 ultrasound machines and found that 69% of the machines had output powers that differed by more than 30% from the reported values. Newer types of transducers, designed to emit at multiple frequencies, performed especially poorly.

Despite the 15 years since the report by Pye and Milford,24 there appears to be little change in the consistency of US output. Recently, Johns et al18 measured the ERA and output power levels of 7 calibrated transducers operating at both 1 and 3.3 MHz from a single manufacturer. Although all 7 ERA values and all 7 output power values fell within FDA guidelines, the SAI values still varied from the digital display by –16% to +25%.18 A follow-up study of 66 transducers from 6 manufacturers operating between 3.0 and 3.3 MHz reported a variation in measured SAI from the digital display by –26% to +19%.20 We have seen no recent reports of these measures performed on transducers operating at 1 MHz. Therefore, the purpose of this technical report is to examine a group of multifrequency transducers operating at 1 MHz to determine the level of variability in ERA, output power, and SAI.


    Methods
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Conclusion
 References
 
Ultrasound Equipment and Calibrations

Sixty-six ultrasound transducers and 6 ultrasound generators able to activate them were purchased from 6 manufacturers (n=11/manufacturer). An a priori power analysis determined the minimum number of transducers required to find statistical significance; manufacturer numbers were limited by the available grant funds. We attempted to test units that are being used clinically. Researcher anonymity was maintained by having the equipment purchased through a third-party therapeutic modality repair vendor who often purchases transducers in bulk. The results of the testing of these transducers at 3.3 MHz have been reported elsewhere.20

The following ultrasound transducer models were examined: Chattanooga (78047*), Dynatronics (#300-5{dagger}), Mettler (ME7513{ddagger}), Omnisound (2303050§), Rich-Mar (C4||), and XLTEK (UL-5#). Prior to measurements, each ultrasound transducer was independently calibrated and tested (Tesco, 40 Old Parish Dr, South Windsor, CT 06074) to within ±15% according to manufacturer guidelines using a wattmeter (model UPM-DT-10**). The test tank was filled with room temperature degassed water. The transducer face was placed parallel to the center of the cone 0.6 cm below the surface of the water. Prior to calibration, the surface of each transducer was checked to ensure that no air pockets or bubbles remained on the surface of the transducer.

Following transducer calibration, the ultrasound generator was set to 5 W on the digital display, and the total wattage produced by each transducer was measured using the wattmeter. All transducers then were shipped to a second laboratory for measurement of the ERA. Following ERA measurement, the transducers were returned to Tesco and remeasured for total watts to ensure that each transducer had remained within calibrations. All transducers had retained calibration. The mean of the 2 measurements is presented as experimental wattage produced when compared with the digital display. Reliability between the repeated wattmeter measurements was good (intraclass correlation coefficient [3,1]=.77, standard error of the measurement=0.23). All wattmeter measurements were collected by a single examiner.

Ultrasonic Measurement System

A hydrophone, which monitors sound underwater, was used to assess ultrasonic output. Both the ultrasound transducer and hydrophone were placed in a tank containing degassed water. Each ultrasound transducer was electrically driven by a gated tone burst generated by laboratory equipment instead of the manufacturers’ driving units; this allowed optimization of the tone burst length and repetition period to minimize tank reverberations and also allowed electronic synchronization between the tone burst and data acquisition (the manufacturer does not provide a "sync out" from the driving unit). Specifically, the transducer was connected to the output of a power amplifier (ENI 440LA, S/N 126{dagger}{dagger}), which was driven by a function generator (HP 3314A{ddagger}{ddagger}). A gate of 100 cycles (for 1 MHz) with a repetition rate of 1.0 kHz provided clean signals without interference from reverberations. Hydrophone measurements were made of each ultrasound transducer's output frequency as driven by the manufacturers’ driving unit, and this output frequency was duplicated with the function generator. Driving amplitudes were adjusted so that the pressure signals were well within the linear range for water (typical root mean square pressure levels were 30 kPa).

A 400-µm-diameter hydrophone (HNZ-0400§§) was connected to a digital oscilloscope (Tektronix 724A||||), which was triggered by the pulse generator. To measure signals representative of the steady-state operation of the transducers, the waveforms were measured at a delay of 85 microseconds relative to the trigger signal, over a time window of 2.5 microseconds. Data were acquired through an automated scanning system (XYZ) manufactured by SEA. A scanning step size of 0.44 mm was used; the positional accuracy of the scanner was ±0.013 mm.

Measurements and Calculation of ERA

The hydrophone was aligned with the beam axis of the transducer and then was systematically positioned and repositioned along a 31-point x 31-point grid at 0.44-mm intervals across the ultrasound transducer under computer control, making a total of 961 measurements. Hydrophone output (in voltage) was converted to pressure using the calibration factor for the hydrophone. Pressure was converted to intensity via the following formula:


Formula 1

(1)
where the acoustic impedance of water=1.5 x 106 rayls. The pulse intensity integral was then computed as:


Formula 2

(2)
where T=the time window over which the pressure is captured. To calculate the ERA, the pulse intensity integral was measured over a planar surface at a distance of 5 mm from the face of the ultrasound transducer (this distance was determined within an accuracy of ±0.1 mm by measuring the time of flight between the trigger signal and the arrival of the pulse). The intensity data were then converted to a decibel scale, relative to the peak intensity, and plotted as a 2-dimensional color map. Effective radiating area was calculated as the area over which the intensity was greater than 5% of the peak intensity.19 The overall accuracy of this algorithm for determining ERA has a complicated dependence on each beam geometry.23 Results from a few repeated measurements, as well as the results of other researchers for similar beam geometries,23 suggest that an uncertainty of ±15% in ERA is reasonable.

Measurement of SAI

Experimental SAI was determined by dividing the experimental output power (in watts) by the experimental ERA (in square centimeters). Dynatronics, Mettler, Rich-Mar, and XLTEK use 5 cm2 as a default ERA setting in their software to calculate SAI; therefore, when the output power is set to 5 W, the machine also reads 1.0 W/cm2 when toggled to SAI. Chattanooga uses 4 cm2 as a default ERA for software calculations; when the output power is set to 5 W, the machine toggles to 1.2 W/cm2. Therefore, to normalize our measured SAI to allow for a direct comparison between manufacturers, the following equation for Chattanooga data was used:


Formula 3

(3)
where 0.8 represents the ratio of the reported ERA to the standardized ERA of 5.0. Omnisound measures and provides transducer-specific ERAs for software calculation of transducer-specific SAIs. To normalize our measured SAIs for Omnisound transducers, the following equation was used:


Formula 4

(4)
where X represents the ratio of the reported ERA to the standardized ERA of 5.0 cm2.

Data Analysis

The Statistical Package for the Social Sciences (version 12.0 for Windows##) was used to generate inferential and descriptive statistics. The 3 dependent variables (ERA, nSAI, and total power) were grouped into a multivariant analysis of variance to determine significant differences between manufacturers. Following a significant Wilks lambda test (P≤.001), the 3 dependent variables were individually analyzed with one-way analyses of variance. A significant Levene test, indicating a lack of homogeneity between the variance of the manufacturers on the ERA and nSAI variables (P≤.01), necessitated conservative Tamhane T2 post hoc testing for final analysis. In addition, reported ERAs and measured ERAs and digital display of SAI and calculated SAI were each compared for each manufacturer using paired t tests. Calculated SAIs were compared with the experimental standard (ie, 1 W/cm2) with single-sample t tests.


    Results
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Conclusion
 References
 
The means and standard deviations for the reported and measured values of ERA and output power are presented in Table 1. All output power values fell within FDA guidelines and manufacturers’ reported specifications. In contrast, ERA values showed large variations. The Rich-Mar transducers had a group mean ERA value that fell outside of the manufacturer's reported range (measured value=3.83±0.21 cm2, reported value=5.0±1.0 cm2), and the Mettler transducers were on the extreme of the acceptable value (measured value=4.01±0.34 cm2, reported value=5.0±1.0 cm2). Five Mettler transducers, 8 Rich-Mar transducers, and 2 XLTEK transducers fell outside of manufacturers’ reported specifications (and thus outside of FDA guidelines).


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Table 1. Measured and Reported Effective Radiating Area (ERA), Output Power, and Normalized Spatial Average Intensity (nSAI) Valuesa

 
There was no significant difference between the reported and the measured values of ERA for the Chattanooga transducers (P=.475), but all other manufacturers had significant differences between reported and measured values (minimum P<.05). Omnisound transducers had the largest range of ERA values (4.1–5.9 cm2); however, this company does report individual ERA values for each transducer. Omnisound was followed closely by XLTEK (range=3.76–5.26 cm2). Chattanooga transducers had the lowest range of values (3.51–4.19 cm2). Inter-manufacturer post hoc testing of ERA and power values is represented by the homogeneous subsets in Table 1. The homogeneous subsets indicate that the comparison values within each subset were not statistically significantly different from one another.

The transducers from different manufacturers produced significantly different nSAI values (P≤.001). Post hoc results are reported in the Figure. Group average nSAI values ranged from 1.39±0.12 W/cm2 for Mettler to 0.84±0.05 W/cm2 for Dynatronics (P<.001). Within-manufacturer variability data are presented in Table 2. Individual transducers ranged from 0.57 W/cm2 for an Omnisound transducer to 1.61 W/cm2 for a Mettler transducer, indicating a range from the digitally reported nSAI values of –43% to +61% within this cohort of 66 transducers (Tab. 2). Intra-manufacturer variability of nSAI ranged up to 53%. Transducers from 5 of the 6 manufacturers had nSAI values that were significantly different from that reported (minimum P=.005). The exception to this difference was Omnisound (P=.068). We attribute this lack of significance to the large standard deviation relative to the group mean.


Figure 1
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Figure. Comparison of group means for normalized spatial average intensity values between manufacturers. Bars indicate standard deviation. *=Mettler is significantly larger than Rich-Mar, XLTEK, Chattanooga, Omnisound, and Dynatronics (minimum P<.007); **=Mettler, Rich-Mar, XLTEK, Chattanooga, and Dynatronics are significantly different from the experimental standard (minimum P<.005); +=Rich-Mar is significantly larger than Chattanooga (P=.034), Omnisound (P=.003), and Dynatronics (P<.001); @=XLTEK is significantly larger than Omnisound (P=.024) and Dynatronics (P<.001); #=Chattanooga is significantly larger than Dynatronics (P<.001).

 

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Table 2. Range of Values for Normalized Spatial Average Intensity (nSAI) Relative to Expected Value of 1.0 W/cm2

 

    Discussion
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Conclusion
 References
 
Variability in the heating potential of different ultrasound transducers is known to exist.11,12 Researchers have suggested that variations in SAI may be a factor in accounting for inconsistencies in patient outcomes. Recent reports have demonstrated significant differences between experimentally measured and generator-displayed SAI values at 3 MHz.18,20 Disparity in SAI depends on variations in the ERA and total output power being delivered. This study is the first to examine new transducers on a large scale, across manufacturers, at 1 MHz.

All transducers fell within the FDA guidelines of ±20% for the total output power emitted. This leads to 2 possible conclusions; either the output power measures are not the major source of SAI variability or the standards controlling the output power measures are too low. One limitation of output power measurement is the variability inherent to the devices measuring this value. The American National Standards Institute requires that the wattmeter used to take the measurements have a minimum of 4 times the accuracy of the unit to be tested.25 Therefore, a minimum wattmeter accuracy of 5% is required to meet the FDA requirement of ±20%. Unfortunately, wattmeter accuracy is limited; the Ohmic wattmeter used in this study has an accuracy of 3%. Therefore, using this wattmeter as the standard, the minimum that the FDA could drop the output power error band to is ±12%. A larger concern with ultrasound output power is the lack of calibration of units in clinical practice. For example, Arthro et al26 recently reported that 39% of the ultrasound machines they tested were outside the permitted error band for output power.

The measurements of ERA were highly varied, with a total of 15 transducers (23%) falling out of manufacturers’ reported guidelines (and thus FDA guidelines). The mean ERA for Chattanooga transducers was well within the reported limits, accompanied by a small standard deviation. This stands in contrast to a previous report20 that Chattanooga transducers, operating at 3.3 MHz, had ERAs at the larger end of the error band, which resulted in the emission of lower-than-displayed SAI values.

In contrast to Chattanooga transducers, the group mean for Rich-Mar transducers was outside of FDA limits (3.85±0.21 cm2) while maintaining a small standard deviation. Rich-Mar would apparently do well to report their ERA as 4.0 cm2 (rather than 5.0 cm2) and make the appropriate output power corrections, as does Chattanooga. Although Mettler transducers met FDA guidelines (4.01±0.34 cm2), this same recommendation to report the batch as 4.0 cm2 also could be made for Mettler (Tab. 1). No individual Mettler or Rich-Mar transducer would have fallen out of FDA guidelines if these manufacturers had reported ERA as 4.0 cm2 rather than the 13 that fell out of the guidelines with an ERA of 5.0 cm2. These lower-than-reported Mettler ERA values are in contrast to Mettler's higher-than-reported ERAs at 3 MHz24; this raises the question about the relationship of ERA values in single crystals designed to operate at multiple frequencies.

Omnisound is the only manufacturer we tested that performs ERA scans on each transducer. Overall, the Omnisound transducers had measured ERA values that coincided with their reported values. There were 2 large variations worth noting. Transducer #28438 reported an ERA of 2.9 cm2, whereas we measured 4.6 cm2; and transducer #28443 reported an ERA of 3.6 cm2, whereas we measured 5.8 cm2. We are unsure why we found such large differences in these 2 transducers from a manufacturer who performs ERA scans on each transducer at both frequencies.

There are great technical challenges in the measurement of ERA27; although we attempted to follow manufacturer's guidelines in the testing of ERA, slight variations are expected based on the details of the technique. Overall, the variability we report in ERA may actually underestimate the true variability in clinical practice as we used a standardized amplifier and function generator to drive the ultrasound transducers during ERA measurements. Therefore, we have not accounted for variability in the electronic circuits of the driving units.

Like the ERA values, our nSAI values had a large range. The individual transducers ranged from –43% to +61% of the digitally displayed value. Although not to the point of the theoretical range of 150% (allowed when ERA and output power deviate maximally within FDA guidelines), this is the greatest range of values we have seen reported for calibrated transducers.18,20 Dynatronics and Omnisound transducers had the lowest group values for nSAI (0.84±0.05 W/cm2 and 0.88±0.20 W/cm2, respectively). Dynatronics transducers produced these numbers due to a combination of larger-than-reported ERA values matched with lower-than-displayed output power values; the Dynatronics transducers were consistently underpowered relative to generator displays. The low Omnisound nSAI was due in large part to the 2 transducers with the low reported ERAs. In these transducers, the low reported ERAs were matched to low output power values; when this low output power was run through a larger ERA, the resulting nSAI dropped greatly. The 2 Omnisound transducers in question had nSAIs of 0.57 and 0.60 W/cm2, respectively, lowest of the entire cohort.

The highest nSAI values came from the Mettler transducers. Despite ERA values that were lower than the manufacturer reports, total output power was consistently higher than on the digital display. As a group, these transducers were overpowered by 39%, with the extreme transducer functioning at 1.61 W/cm2 when the digital display read 1.0 W/cm2. These Mettler values are in stark contrast to the 3-MHz values reported by Johns et al,20 where the group average for Mettler transducers was almost perfect with a mean of 0.99±0.08 W/cm2. In contrast to Mettler, Rich-Mar transducers matched their smaller ERAs with lower output power values. The result is that the group exceeds the digital display by only 21%, with the extreme transducer at 1.30 W/cm2.

Even small differences in SAI have the potential to cause changes in tissue heating. Demchak et al28 have reported that, at 1 MHz, differences in SAI as small as 0.2 W/cm2 may alter the heating curve. The variation predicted when using the Mettler transducers is even more profound. Based on the heating rates published by Draper et al,5 if a clinician planned to provide a 1-MHz ultrasound treatment at 1.0 W/cm2 for 10 minutes with the goal of increasing tissue temperature (at a depth of 2.5 cm) by 1.5°C, use of Mettler transducer #486 (ie, the one with the lowest SAI among those we tested: 1.2 W/cm2 while the digital output read 1.0 W/cm2) might evoke a temperature rise close to 2.5°C. In contrast, use of Mettler transducer #167 (ie, the one with the highest SAI among those we tested: 1.61 W/cm2 while the digital output read 1.0 W/cm2) would likely evoke a rise greater than 3.5°C. These differences would greatly influence tissue response, as the heating levels went from a desired level of mild heating to vigorous heating.

The ERA and SAI differences we report may help explain a report of heating differences at 1 MHz. Kimura et al4 compared an XLTEK transducer to a Mettler transducer while heating phantom tissue. The ultrasound units were new, calibrated by the manufacturers, and output power was confirmed by a wattmeter to be within FDA standards. Despite the care taken to control the ultrasound units, at the end of a 5-minute treatment, the XLTEK transducer heated the tissue 0.80±0.14°C on average, while the Mettler transducer heated the tissue to 1.48±0.28°C. Kimura et al were hard-pressed to explain this occurrence. We now suspect that despite equal SAI settings and expectations, the Mettler transducer may have delivered more output power over a smaller area, resulting in the greater heating.

The clinical efficacy of therapeutic ultrasound is a topic for debate. Although ultrasound is commonly used during physical rehabilitation, there are at least 3 systematic reviews3,29,30 currently available that indicate that there is little evidence to support the use of therapeutic ultrasound for musculoskeletal injury. We would argue that the question of clinical efficacy may be premature, because the question of accurate clinical dosing has yet to be answered. Inaccurate measures of ERA will affect SAI and also may affect treatment area, as some authors have suggested treating an area 2 to 3 times the ERA. Omnisound is the only manufacturer represented that measures the ERA for all transducers and consequently their nSAI values do not significantly differ from the experimental standard. Despite this, they still have large intra-manufacturer variability in the nSAI output. Manufacturers must develop more efficient and consistent methods of ERA measurement or develop treatment parameters that are not dependent upon this metric.


    Conclusion
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Conclusion
 References
 
Large variability exists in SAI values (both within and between manufacturers) at 1 MHz. The variability is largely the result of inaccurate measurements of ERA and also the result of large permitted variation in measurements of output power (in a calibrated sample). The range of measured values at 1 MHz is much greater than previously reported for US at 3 MHz. Manufacturers must take more care in reporting proper ERA values. Accurate measures of ERA, output power, SAI, and energy dosing are critical when developing studies to determine clinical efficacy and attaining consistent clinical outcomes while using therapeutic ultrasound.


    Footnotes
 
Dr Straub and Dr Johns provided concept/idea/research design and writing. All authors provided data collection and analysis. Dr Johns provided fund procurement. Dr Howard provided consultation (including review of manuscript before submitting).

This project was supported by a grant from the National Athletic Trainers’ Association–Research and Education Foundation, Dallas, Tex.

This study was presented at the 54th National Athletic Trainers’ Convention and Clinical Symposium; Indianapolis, Ind; June 2005, and was published in abstract form in Journal of Athletic Training, 2005;40(2):S51.

Dr Howard is an employee of Onda Corp, which is a potential vendor of hydrophone systems to the manufacturers of the equipment used in this study.

* Chattanooga Group, 4717 Adams Rd, Hixson, TN 37343. Back

{dagger} Dynatronics, 7030 Parke Centre Dr, Salt Lake City, UT 84121. Back

{ddagger} Mettler Electronics, 1333 S Claudina St, Anaheim, CA 92805. Back

§ Accelerated Care Plus, 4850 Joule St, Reno, NV 89502. Back

|| Rich-Mar Corp, 4120 South Creek Rd, Chattanooga, TN 37406. Back

# XLTEK, 2568 Bristol Cir, Oakville, Ontario, Canada L6H 5S1. Back

** Ohmic Instruments, 508 August St, Easton, MD 21601. Back

{dagger}{dagger} MKS Instruments, 100 Highpower Rd, Rochester, NY 14623. Back

{ddagger}{ddagger} Agilent Technologies Inc, 5301 Stevens Creek Blvd, Santa Clara, CA 95051. Back

§§ Onda Corp, 592 Weddell Dr, Ste 7, Sunnyvale, CA 94089. Back

|||| Tektronix Inc, 14200 SW Karl Braun Dr, Beaverton, OR 97077. Back

## SPSS Inc, 233 S Wacker Dr, Chicago, IL 60606. Back


    References
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Conclusion
 References
 

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