Abstract
PURPOSE
Due to host-mediated adverse reaction to metallic debris, there is an increasing need for noninvasive assessment of the soft tissue surrounding large joint arthroplasties. Quantitative T2 mapping can be beneficial for tissue characterization and early diagnosis of tissue pathology but current T2 mapping techniques lack the capability to image near metal hardware. A novel multi-spectral T2 mapping technique is proposed to address this unmet need.
METHODS
A T2 mapping pulse sequence based on routinely implemented 3D multi-spectral imaging (3D-MSI) pulse sequences is described and demonstrated. The 3D- MSI pulse sequence is altered to acquire images at two echo times. Phantom and knee experiments were performed to assess the quantitative capabilities of the sequence in comparison to a commercially available T2 mapping sequence. The technique was demonstrated for use within a clinical protocol in two total hip arthroplasty (THA) cases to assess T2 variations within the periprosthetic joint space.
RESULTS
The proposed multi-spectral T2 mapping technique agreed, within experimental errors, with T2 values derived from a commercially available clinical standard of care T2 mapping sequence. The same level of agreement was observed in quantitative phantoms and in-vivo experiments. In THA cases, the method was able to assess variations of T2 within the synovial envelope immediately adjacent to implant interfaces.
CONCLUSION
The proposed 3D-MSI T2 mapping sequence was successfully demonstrated in assessing tissue T2 variations near metal implants.
Keywords: Metal Implants, T2 Mapping, multi-spectral imaging
INTRODUCTION
The number of arthroplasty procedures performed to alleviate pain and improve function from chronic joint disorders continues to increase at a rapid rate, which has led to a correlative increase in subsequent revision surgery [1]. The inherent soft tissue contrast of magnetic resonance imaging (MRI) makes it the most suitable imaging technique to assess post-operative joint integrity in arthroplasty cases [2, 3, 4]. Metal induced susceptibility artifacts, however, make it difficult to image near such hardware [5, 6]. Though two-dimensional fast/turbo spin echo techniques acquired with small voxels and with higher readout encoding bandwidths can reduce artifacts, diagnostic capabilities near implants are still often compromised [7]. The Multi-Acquisition with Variable Resonance Image Combination (MAVRIC) [5], Slice Encoding for Metal Artifact Correction (SEMAC) [8], and MAVRIC-SL hybrid [9] methods are the most commonly utilized three-dimensional multi-spectral imaging (3D-MSI) techniques. 3D-MSI techniques acquire multiple volumes at different frequency offsets from the Larmor frequency. These volumes, or “spectral bins”, are then combined to form a composite image which has minimal susceptibility artifacts.
Arthroplasty procedures can lead to complications such as periprosthetic fracture, mechanical loosening, implant wear, osteolysis, synovitis, and component mal-positioning [3, 2, 10]. Early diagnosis of these com- plications can minimize the tissue destruction associated with these adverse local tissue reactions and the subsequent morbidity at revision surgery, also acting to reduce treatment costs. Standard MRI evaluation of tissues near arthroplasty utilizes morphological imaging [11], and can only provide a qualitative description of joint health. Quantitative parametric mapping techniques are a noninvasive tool to evaluate tissue integrity and report bio-markers that are indicative of tissue health. T2 mapping has been shown to be useful in assessing tissue hydration and orientation of collagen in articular cartilage [12, 13, 14] and is now an established bio-marker for detecting early-stage osteoarthritis [15]. A motivating application for the present study is the use of T2 mapping in assessing soft tissue and bony pathology near total hip arthroplasty. Specifically, it is hypothesized that susceptibility artifact suppressed T2 maps could provide insight on fibrous membrane formation at implant interfaces. Furthermore, with sensitivity to fluid content and other macro-molecular variations, T2 maps could aid in classifying types of host- mediated adverse local tissue synovial reactions near arthroplasties.
Multiple approaches can be utilized to acquire T2 maps. Spin-echo based maps utilizing multiple refocused signals collected at different echo times are commercially available on GE (CARTIGRAM) [16] and Siemens (MapIt) platforms. (3D Magnetization-Prepared Angle-Modulated Partitioned k-Space Spoiled Gradient Echo Snapshots) 3D MAPSS is a non-commercial sequence that uses preparation modules on a 3D gradient echo acquisition for T2 maps [17]. These two approaches are the most common T2 mapping methods utilized for orthopedic applications. CARTIGRAM and MapIt are 2D multi-echo spin echo pulse sequences that collect several echoes per phase-encoded line. The long acquisition time of these techniques renders them non-viable for collecting the multi-spectral data required for imaging near implants. The 3D MAPSS technique is a spoiled gradient echo based technique, and thus cannot be used for imaging soft tissues immediately adjacent to metal implants, due to its substantial T2 * signal loss experienced near implant interfaces. To date, the application of susceptibility artifact suppressed T2 mapping near metal implants has yet to be demonstrated.
In this work, a dual-echo multi-spectral 3D fast spin echo (3D-FSE) based T2 mapping pulse sequence for imaging near metal hardware is described and demonstrated. Specifically, the sequence was developed by modifying the MAVRIC SL 3D-MSI pulse sequence to serially acquire images at two echo times within a single scan prescription. The presented approach could be extended to collect more echo images. However, the analysis in this work was limited to dual-echo acquisitions in order to assess the performance of a clinically reasonable acquisition that could be acquired in approximately 6.5 minutes.
A controlled phantom experiment was performed to compare the relaxometry measurements made with the 3D-MSI T2 mapping sequence in both a clinically non-viable 9-echo form (requiring approximately 36 minutes of acquisition time) and dual-echo form (clinically viable). This experiment allowed for an assessment of potential inaccuracies introduced by the relaxometry measurement. Both 3D-MSI based approaches were then compared to a commercially available approach (CARTIGRAM).
The proposed dual-echo 3D-MSI approach and CARTIGRAM were also applied in vivo in a contrived experiment that allowed for mapping of cartilage with and without the presence of metallic artifact. Finally, the dual-echo 3D-MSI approach was applied within a clinical examination on two total hip replacement patients to test the applicability of the sequence in the clinical setting. This allowed for T2 quantification within the periprosthetic joint space which is sensitive to structural and tissue changes.
METHODS
Pulse sequence development
The methods used in this study are based upon the MAVRIC-SL 3D-MSI pulse sequence, which is a multi-spectral 3D fast spin echo imaging sequence [18, 19]. This multi-spectral approach uses excitation and the refocusing RF pulses that are Gaussian shaped with a full width at half maximum ratio of 2.25 kHz, bin separation 1 kHz and a readout bandwidth of ±125 kHz. Typically, the refocusing flip angles ranging between 110o - 135o are used to reduce the specific absorption rate (SAR) of the sequence while allowing for comparatively broadband refocusing to be applied. In order to reduce acquisition times, the MAVRIC SL 3D-MSI technique utilizes partial-Fourier acquisition, which further necessitates the use of a radial phase-encoded ordering scheme, as presented by Busse et al [20]. Effective echo times can be adjusted in this approach using the coherence pathway analysis also presented by Busse et al, along with the application of null-encoded (skipped) echoes in the front end of the echo train, as illustrated in Figure 1a.
FIGURE 1.
Pulse sequence diagram for the Multi-series 3D-MSI(a) and the modified dual-echo 3D-MSI(b) techniques: Constant flip angle train, and data acquisition for 2 echo times are the main differences between the 3D-MSI and the modified dual-echo 3D-MSI sequence. The encoding and readout gradients timings are adjusted to account for the desired TEs as shown in (b).
Modified dual-echo 3D MSI pulse sequence
The pulse sequence diagram for the modified dual-echo pulse sequence is presented in Figure 1b. In order to acquire the full complement of spectral bins for the second echo time, the number of passes are doubled and number of echoes to be skipped before the start of data acquisition are recalculated. The two rows below the RF wave-forms in Figure 1b (rows in blue) show the acquisition scheme for echo time 1 (TE1 ), while the last two rows (in red) show the acquisition scheme for echo time 2 (TE2 ).
The total echo train length (ETL) in the acquisition is the prescribed ETL plus the number of skipped (null-encoded) echoes. The number of skipped echoes depends on the longest echo time, which is TE2 . The first half of the sequence encodes for TE1 whereas the second half of the sequence encodes for TE2 . Accordingly, the phase/slice encoding and the data acquisition are adjusted as shown in the bottom two rows. This type of encoding requires a constant refocusing flip angle train to quantify the signal obtained from both echo times accurately. In this case, a constant refocusing flip angle train of 110o was used. In addition, use of refocusing flip angles less than 180o , leads to oscillations in the signal intensity for initial echoes before pseudo steady-state is achieved [20]. Hence, in this relaxometry application, the minimum number of skipped echoes is empirically estimated for a minimum effective echo time (TE1 ). The number of echoes to skip for the first acquired echo-time (TE1 ) image in the dual-echo sequence was empirically found and set to 3 for all the experiments. The number of echoes skipped for the second echo-time image was calculated to be 9 echoes for the echo time of 55ms.
Imaging Experiments
Phantom and knee volunteer datasets were acquired on a GE Healthcare (Milwaukee, WI) Discovery MR 750 3T MR system. Signal acquisition was performed using a Nova Medical 32 channel head coil (phantom) and 8 channel knee coil (knee). Hip datasets acquired on clinical research subjects were acquired on a GE Discovery 1.5T system using an 8 channel cardiac array. The study was approved by respective local Institutional Review Boards. Written informed consent was obtained from all subjects prior to their participation in the study.
Phantom Scanning
A vendor-provided T2 quantification phantom was utilized for bench experiments. The phantom has 6 vials with 2 vials each filled with 2%, 3% and 4% agarose gel. Pulse sequence parameters for the multi-series 3D MSI sequence and modified dual-echo 3D MSI pulse sequence in the phantom experiments were: field of view (FOV) = 16cm, matrix size = 128 × 128, repetition time (TR)= 5s, flip angle = 110o , echo train length (ETL) = 20, auto-calibrated parallel imaging factor = 2, and four 4 mm slice encodes. The data was collected with 9 different echo times (10.04ms, 17.76ms, 21.3, 27.99ms, 31.94ms, 39.5ms, 42.746ms, 50ms and 53.9ms) for the serial multi-experiment 3D MSI acquisition, whereas 2 echo times (21.3ms and 53.9ms) were collected with the modified single-acquisition dual-echo sequence. The number of echoes skipped was 3 and 9 for the two echo times respectively. CARTIGRAM maps were collected using identical parameters as the 3D MSI acquisitions, with the following exceptions: a multi-echo refocused train of 8 echoes was utilized with TE values of (6.25ms, 12.5ms, 18.75ms, 25ms, 31.25ms, 37.5ms, 43.75ms, 50ms) and a repetition time of 1.2s. Acquisition times were (min:sec) (36:00) for multi-experiment 3D MSI (cumulative), (8:01) for dual-echo single-acquisition 3D MSI, and (5:10) for CARTIGRAM.
The T2 maps were computed from multi-echo data using a mono-exponential fit. Magnitude imaging data were transformed to a natural logarithmic space. For the methods with more than two echoes, T2 values were derived from slopes computed using simple linear regression methods (MATLAB, Mathworks, Natick, MA). For the dual-echo acquisition, the T2 value was calculated using a simple closed-form exponential equation. The results from both the 3D-MSI sequence acquired sequentially with different echo times and the modified single-acquisition dual-echo pulse sequence were compared with each other and with CARTIGRAM. The percentage differences of T2 between the CARTIGRAM, multi-series 3D-MSI, and dual-echo 3D-MSI were calculated for each vial within the phantom.
Subject Scanning
An in-vivo dataset was acquired on a knee using a large externally positioned cobalt chrome implant (50mm diameter total hip resurfacing acetabular component) to allow for controlled tests with and without metal artifact at 3T. The implant was positioned to provide substantial artifact in conventional (non 3D-MSI) techniques within the trochlear cartilage region. The following imaging parameters were used for all acquisitions: FOV: 16 cm, matrix size = 192 × 128, slice thickness = 2.5 mm, TR = 4s, and 16 slices. CARTIGRAM imaging acquired 8 TE images: 6.25ms - 50ms with ∆ TE =6.25ms, and dual-echo 3D-MSI acquired 2 TE images: 21.72ms, and 55ms. An in-plane phase acceleration of 2 was used. When the metallic implant was placed in the field of view, 16 spectral bins were collected. T2 values were calculated using the methods as described above. Regions of interest were manually selected within the articular cartilage and muscle to generate summary statistics (mean ± SD). The percentage difference of T2 between the CARTIGRAM without metal present and the other sequences (CARTIGRAM with metal present, 3D-MSI without metal present, 3D-MSI with metal present) were calculated for the defined cartilage and muscle regions.
In addition, a single-acquisition dual-echo 3D-MSI T2 mapping dataset was collected on two total hip replacement patients undergoing clinical MRI examinations of tissues near their implanted devices. Imaging parameters for these acquisitions were: FOV: 42 cm, matrix size = 512 × 256, slice thickness =3.5 mm, and 24 slices. Auto-calibrated phase-encoded acceleration factors of 2×2 were used to collect 16 spectral bins. The number of echoes skipped were 3 (for TE1 ) and 8 (for TE2 ) which resulted in echo times of 9.5ms and 50ms respectively. The acquisition time for the dual-echo 3D-MSI T2 maps on total hip replacements was approximately 6.5 minutes.
RESULTS
Phantom Scanning
The mean T2 values obtained from the 3 approaches were in good agreement with each other, with a maximum difference of approximately 10% (Table 1). Quantitative comparisons of the signal decay between CARTI-GRAM, multi-series 3D MSI and the modified dual-echo 3D MSI T2 mapping sequences collected on the T2 phantom are shown in Figure 2. It is noted that the multi-series 3D-MSI approach and the dual-echo approach have similar computed decay trends and T2 values. This is a fortunate observation, as the shorter dual-echo approach is required for acquisition of 3D-MSI relaxometry maps within clinically acceptable time frames.
TABLE 1.
Mean T2 values and standard deviations (in ms) for the vials with 2%, 3% and 4% agarose gel indicated in Figure 2 are given here. The T2 values obtained from the Multi-series approach and the dual-echo approach yield similar results and are within 10% error with respect to CARTIGRAM. Note: the scan times for CARTIGRAM, Multi-series 3D MSI and Dual-echo 3D MSI are (MIN:SEC) (5:10), (36:00), and (8:01) respectively. The percent errors with respect to CARTIGRAM are given in the brackets.
| CARTIGRAM | Multi-Series 3D MSI | Dual-Echo 3D MSI | |
|---|---|---|---|
| Vial1 | 76 ± 2 | 72 ± 2 (5.5%) | 72 ± 2 (6%) |
| Vial 2 | 54 ± 2 | 50 ± 1 (8%) | 50 ± 1 (9%) |
| Vial 3 | 44 ± 1 | 39 ± 1 (10%) | 40 ± 1 (9%) |
FIGURE 2.
Phantom experiment results: The signal decay as function of echo time is shown in the plots for CARTIGRAM, Multi-series 3D-MSI and Dual-echo 3D-MSI sequences for each vial. The signal decay is similar for all the three sequences in all the three vials. The T2 values for this experiment are given in Table 1. Note: The 2%, 3% and 4% agarose gel concentrations provide different T2 values for quantitative mapping comparisons.
Subject Scanning
The mean T2 values of articular cartilage for 3D-MSI with and without metal present were less than 4% different than corresponding measures made using CARTIGRAM. The mean T2 values of muscle for 3D-MSI without metal present were 11.6% higher than similar CARTIGRAM measurements, and were 19% higher when metal was present. A pictorial display of source images and associated T2 maps of the CARTIGRAM and 3D-MSI techniques with and without metal present is shown in Figure 3. CARTIGRAM T2 mapping with metal present was not possible since through-slice signal distortions completely obscured the trochlear cartilage.
FIGURE 3.
In-vivo evaluation of the modified dual-echo 3D MSI sequence in knee: The top row shows a T2 weighted image for CARTIGRAM with and without the presence of metal and modified 3D-MSI sequence in the presence of metal in knee as seen in (a), (b) and (c) respectively. The T2 map for the trochlear cartilage obtained using CARTIGRAM (d), Modified dual-echo 3D-MSI without (e) and with (f) metal are seen in the bottom row. The trochlear cartilage is completely obscured in CARTIGRAM near metal (b) due to the metal induced susceptibility as seen by the white arrow.
The modified dual-echo sequence demonstrated on two patients with total hip arthroplasty (THA) is seen in Figure 4. Radiological analysis of the morphological images and associated T2 map suggest that Region 1 is a synovial tissue compartment showing lower T2 , which suggest a lower fluid content. Region 2 appears to be extra-capsular fat, which is confirmed by its longer T2 estimate [21]. Region 3 appears to be the short external rotator tendon which is confirmed by its shorter T2 value. Similar to region 2, region 4 is extra-capsular fat with a longer T2 value.
FIGURE 4.
In-vivo application of the modified dual-echo 3D-MSI sequence in patients with total hip replacement: A T2 -weighted image (a, c) and the corresponding T2 maps (b, d) for the two patients are shown. The mean and the standard deviation of the T2 values for four ROIs shown above (1,2,3,4) are 55 ± 13ms, 104 ± 11ms, 54 ± 9ms and 104 ± 10ms respectively.
DISCUSSION
In this work, a technique for performing T2 relaxometry near metal implants is presented. This approach leverages a modified dual-echo 3D-MSI pulse sequence to acquire images at two echo times with identical spectral bin sampling. A challenging limitation of this approach is estimation of effective echo times in FSE/TSE echo trains utilized to collect the dual-echo time spectral bin sets. Other approaches to T2 relaxometry, such as the commercial CARTIGRAM technique, utilize refocused echoes with fixed echo spacing. While this approach can allow for a simpler T2 relaxometry approach, it is extremely inefficient and has acquisition times comparable to single spin echo approaches. When applied to multi-spectral imaging, such an approach would result in relaxometry acquisition times that may exceed 30 minutes or longer, which is not clinically viable.
In the current study, the phase-graph coherence analysis presented by Busse et al [20] was utilized to estimate effective echo times for the utilized 3D-MSI data. Close examination of Figure 2 shows that the first two echo-time signals of the multi-series 3D-MSI technique consistently deviate from the expected exponential decay trend. The reason for this is that that these echoes are acquired before the collected signal achieves pseudo steady state. The T2 maps recalculated by skipping first three echoes in this dataset are presented in online Supporting information Table S1. In this controlled multi-echo time 3D-MSI experiment, it was observed that the signal stabilizes after 3 echoes. Hence, the dual-echo 3D-MSI application used for all experiments in this study skipped a minimum of 3 echoes. An alternative approach to reduce the problematic early signal oscillations would be to modify the flip angle of the first refocusing pulses as proposed by Hennig et al [22].
It is noted that the mean T2 values within the muscle ROI for the knee case showed an increased mean error compared to the phantom or trochlear cartilage estimates. However, the increased variance within the ROI kept the estimated T2 values within errors of the CARTIGRAM estimate. These observations warrant further investigation into the cause of increased variance relative to the other measurements in this study.
Simulations indicate that noise results in approximately 5% error in the estimation of T2 values using the current dual echo acquisition. Details on the simulation are provided in the Supporting information figure S1. Future work will explore the use of differing dual echo time settings for application-specific T2 mapping needs.
An alternative technique commonly used to acquire T2 maps adds a T2 preparation module, which is the approach utilized in the MAPSS or CUBE-Quant approaches to T2 relaxometry [17, 23]. Such preparation modules rely on refocusing pulses with flip angles of 180o and non-overlapping spectral profiles with sharp transition profiles. For multi-spectral imaging, tightly-aligned box-car spectral profiles lead to increased spectral bin combination artifacts, and smoother profiles are commonly utilized to address this consideration [9]. In addition, broadband refocusing profiles are typically utilized in 3D-MSI to reduce the required number of spectral bins. Radio frequency amplifier or SAR limits typically limit the flip-angles that can be applied with such pulses, which are typically much lower than 180 degrees. For these two reasons, (flip angles and spectral profiles), T2 preparation modules are not suitable for use with 3D-MSI techniques.
Although the preliminary results of this study are promising, there are a few limitations that require further consideration. First, there is an increase (doubling) of acquisition times compared to conventional 3D-MSI techniques. Acquisition times can be reduced by increasing the echo train length or by increased acceleration levels. Increases in the echo train length will introduce blurring of maps that may still be tolerable for regional quantitative evaluation. Increased levels of conventional parallel imaging and/or compressed sensing will also be explored to further reduce scan time.
There are a variety of applications for the proposed methods. First, relaxometry in instrumented cartilage repair cases would be feasible in the immediate vicinity of screws and fixation pins. Second, as demonstrated in this study, relaxometry of soft tissues near total joint arthroplasty is now feasible. In the case of hip arthroplasty, T2 relaxometry may provide a useful measure of fluid levels and macromolecular changes in different states of synovial inflammatory responses. Of particular interest, the T2 relaxometry may provide specificity to early synovial or adverse local tissue reactions that eventually lead to tissue necrosis and destruction. Further work will be required to assess the sensitivity and specificity of regional T2 values to soft tissue disease progression near total hip arthroplasty. Additionally, this technology could facilitate monitoring and categorization of fibrous membranes along joint interfaces, which represent a failure of implant integration with the surrounding bone. In cases of device loosening, fibrous membranes encapsulating implants are not visible radiographically until they have grown to moderate thickness. Such membranes can be qualitatively identified earlier using 3D-MSI MRI. The use of 3D-MSI T2 maps could aid in early detection of fibrous membrane formation.
In conclusion, the proposed T2 mapping technique provides an additional quantifiable metric to assess tissue near metal implants. In this study, the accuracy and potential utility of the technique has been demonstrated on phantom and in-vivo datasets. Ongoing investigations will continue to translate this approach to clinical cohorts in order to assess its value in diagnostic practice.
Supplementary Material
SUPPORTING INFORMATION TABLE S1 Psuedo steady state analysis for the phantom experiment: The T2 values (in ms) calculated by skipping first echo, first two echoes and first 3 echoes are shown in columns 3, 4, and 5 respectively. The CARTIGRAM T2 values are given in column 2 for reference. The oscillatory behavior of the signal in the pre-psuedo steady state (first few echoes) results in oscillations in the T2 values. We notice that the signal stabilizes after three echoes and hence, the number of echoes to skip for the first acquired echo in the dual-echo approach was set to 3 for the in-vivo experiments.
SUPPORTING INFORMATION FIGURE S1 The supporting information figure S1 shows the percent error in the estimated T2 values as the effect of noise. For T2 values less than 150 ms, the estimation error due to noisy data is less than 5%. The percent error increases with increase in assumed T2 values. Note: The echo times chosen in this simulation are not appropriate for estimation of longer T2 values.
TABLE 2.
Mean T2 values (in ms) and standard deviations for Knee experiment in Figure 3: The T2 values for muscle and trochlear cartilage in Knee obtained from CARTIGRAM, Dual-echo 3D MSI sequence with and without metal are seen here. The percent errors with respect to CARTIGRAM are given in the brackets.
| CARTIGRAM | Dual-echo 3D MSI without metal | Dual-Echo 3D MSI with metal | |
|---|---|---|---|
| Trochlear cartilage | 49 ± 8 | 50 ± 10 (4%) | 47 ± 6 (2.5%) |
| Muscle | 42 ± 4 | 47 ± 4 (12%) | 50 ± 4 (19%) |
ACKNOWLEDGEMENTS
Research reported in this publication was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases (NIAMS) of the National Institutes of Health (NIH) under award number R01AR064840. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH. Funding for this work was also provided by GE Healthcare and the Advancing a Healthier Wisconsin Research and Education Council.
Funding information
National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant/Award Number R01AR064840 GE Healthcare Advancing a Healthier Wisconsin Research and Education Council Word Count 3355
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Associated Data
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Supplementary Materials
SUPPORTING INFORMATION TABLE S1 Psuedo steady state analysis for the phantom experiment: The T2 values (in ms) calculated by skipping first echo, first two echoes and first 3 echoes are shown in columns 3, 4, and 5 respectively. The CARTIGRAM T2 values are given in column 2 for reference. The oscillatory behavior of the signal in the pre-psuedo steady state (first few echoes) results in oscillations in the T2 values. We notice that the signal stabilizes after three echoes and hence, the number of echoes to skip for the first acquired echo in the dual-echo approach was set to 3 for the in-vivo experiments.
SUPPORTING INFORMATION FIGURE S1 The supporting information figure S1 shows the percent error in the estimated T2 values as the effect of noise. For T2 values less than 150 ms, the estimation error due to noisy data is less than 5%. The percent error increases with increase in assumed T2 values. Note: The echo times chosen in this simulation are not appropriate for estimation of longer T2 values.