Fat Fraction Bias Correction using Flip Angle Mapping and Estimated T 1 values

Fat Fraction Bias Correction using Flip Angle Mapping and Estimated T 1 values Issac Yang 250475220 Supervisor: Dr Charles McKenzie Introduction Non-alcoholic fatty liver disease (NAFLD) is rapidly becoming the most common chronic liver disease worldwide, afflicting 20-30% of the general population of western countries [1]. It is also currently the most common liver disease in children [2]. NAFLD refers to a wide spectrum of liver damage, which begins with simple steatosis (accumulation of triglyceride filled vesicles in liver cells), and can progress to non-alcoholic steaohepatitis (NASH), which is characterized by fibrosis and cirrhosis in addition to steatosis and can ultimately lead to liver failure [3, 4]. NAFLD is now classified as part of the metabolic syndrome and is associated with other conditions such as central obesity, type 2 diabetes mellitus and hyperglycemia [3, 5]. NAFLD is largely asymptomatic. The current gold standard for diagnosis and staging of NAFLD is histological analysis of liver biopsies [3, 5]. This makes screening NAFLD, especially in pediatric cases, extremely difficult. Liver biopsy, being an invasive procedure, is associated with complications that range from minor bleeding through hemorrage that requires blood transfusion and hospitalisation, and in rare cases results in death [6, 7]. Furthermore, liver biopsies are very prone to sampling variability due to the inhomogeneous distribution of steatosis in the liver [8]. As a result, techniques enabling the ability to assess steatosis noninvasively throughout the entire liver volume are highly desirable, as they would allow early detection of NAFLD and quantification of heptatic steatosis without the complications and inaccuracy of liver biopsy. Fat and water images generated from chemical shift based fat-water decomposition methods with MRI have been used as a non-invasive alternative to clinically quantify fat fraction in the liver, allowing physicians to be able to detect and monitor the progress of steatosis without performing biopsies [9-11]. Iterative Decomposition of water and fat with Echo Asymmetry and Leastsquares estimation (IDEAL) provides a robust method for separating fat and water signals. Coupled with Spoiled Gradient echo (SPGR), allows for rapid acquisition of images [12, 13]. A fat fraction map can then be generated using the fat and water images. However, due to the difference in spin-lattice relaxation time (T 1 ) for fat and water protons, the weighting for fat and water signals in the fat fraction map will be different, resulting in a bias in fat fraction and causing overestimation of its true value [14, 15]. Several methods currently exist to reduce or eliminate the T 1 bias. However, they are not without their own problems: fat and water densities can be obtained using Driven Equilibrium Single Pulse Observation of T 1 and T 2 (DESPOT) [16] by fitting multiple images acquired at different flip angles thereby eliminating the T 1 reliance in the signal. However, using DESPOT also means multiple images are required within a single breath hold, which is hard to achieve without other means of accelerating acquisition speed. The longer time required to acquire the multiple images also results in a lower signal to noise (SNR) efficiency [17]. DESPOT also requires

knowledge of the true flip angles used. This information may not be known because of inhomogeneities in radio frequency (RF) fields used to generate the flip angles when performing MRI at magnetic field strengths of 3T and above [18]. It is known that the influence of T 1 on signal strength is proportional to the flip angle used to acquire the image. Hence, another method to minimize T 1 bias is to acquire a single image using a small flip angle, thereby reducing T 1 contribution to the signal and reducing bias [14].. However, by reducing T 1 weighting also sacrifices SNR, which causes an elevation of fat fraction noise at extremely low and high fat fractions. This is particularly troublesome when diagnosing a patient for NAFLD onset, as the onset of the disease occurs at a fat fraction of roughly 5% [19]. The relationship between proton density and T 1 and their contribution to the acquired signal is known. Therefore, if T 1 is known, the bias can be eliminated. Although T 1 measurements cannot be performed and precise knowledge of such value is currently clinically unobtainable with any clinically useful methods, an approximation can be made by using values obtained from literature [20]. As such, it is possible to use the obtained T 1 value as a correction factor with the signal equation to decrease the fat fraction bias. Theoretically, this method will allow the usage of higher flip angles while retaining reduced bias from the low flip angle technique. Like the small flip angle method, only a single acquisition is required, thus allowing images to be more easily acquired within a single breath hold and avoiding the longer acquisition time associated with DESPOT. This proposed method, like DESPOT, requires knowledge of the flip angle used. As such, we propose that this technique can be improved by incorporating rapid flip angle mapping to improve the correction. The purpose of this study is to investigate the effect of bias correction by incorporating rapid flip angle mapping along with the aforementioned T 1 estimation to correct for fat fraction bias. Flip angle mapping is performed with a double angle Look-Locker method [18]. Usage of a rapidly acquired flip angle map in place of assumed uniform flip angle throughout the slice will theoretically reduce the amount of residual bias that remains after correction. Initial investigation was performed using numerical simulations. Quantitative empirical analysis was performed on fat/water phantoms. Theory: Fat accumulation in the liver primarily consists of triglycerides. Ideally, the true fat fraction ( is defined as the fraction of fat protons within a voxel: [1] where M w and M f are the proton densities of water and fat, respectively. IDEAL uses multiple images acquired at different echo times (TE) to separate the water and fat signals [11]. Hence, pixel values on the fat fraction map are calculated as the fraction of signal attributed by fat protons in each voxel:

Ideally, the fat and water signals should be proportional to the proton density in the pixel. However, due to the difference in T 1 of fat and water, the weighting of proton density in the signals will be different. As a result, the fat fraction obtained by using the obtained signals will differ from the true fat fraction. With SPGR acquisitions, the signals measured are defined by the following: [2] [3] where α is the flip angle used, and TR is the repetition time between flip angles and M is the volume of either water or fat protons in the voxel. In 3.0T magnetic fields typical in vivo T 1 values for the liver are 809ms for water (T 1w ) and 343ms for fat (T 1f ) [20]. Due to the shorter T 1 of fat protons, fat and water signals will have uneven weighting in the fat fraction equation. This causes the fat fraction map to overestimate the fat fraction of the subject. As seen in EQ 3, the weighting of T 1 contribution to the acquired signal increases with flip angle used. Therefore, higher flip angles will disproportionally increase the signal acquired from fat protons compared to water protons, and thus increase the overestimation of fat fraction. This is demonstrated in the simulated image acquisition shown in FIG 1. FIG 1. Simulated fat fraction acquisitions using flip angles of 10 and 20 degrees, using imaging parameters of T 1w =809ms, T 1f =343ms, TR=7.4ms for acquisitions in 3.0T. The deviation of measured fat fraction from true fat fraction increases with flip angle The low bias associated with low flip angle is the reason why the small flip angle method was proposed. However, the effect of noise must be taken into account. It is evident from EQ 3 that signals acquired from low flip angle will be weaker compared to a higher flip angle due to loss of T 1 contribution to the signal. When noise is being considered, the trade off of using a small flip

angle is evident: reduced bias is accompanied by a decrease in SNR, especially at lower fat fractions. This is shown in FIG 2. FIG 2. Simulated noise of fat fraction after addition of Gaussian noise to fat and water signals. Monte-Carlo simulation was performed (2000runs with T 1w =809ms, T 1f =343ms, TR=7.4ms at fat fractions of 5% and 40%). Gaussian width of noise corresponded to the noise of pure water signal at its Ernst angle (7.8 o, TR=7.4ms, T 1 =809ms) with SNR of 20. It should be noted that noise performance is best at a flip angle of between 7 o and 10 o (FIG 2). This flip angle is a weighted average of fat and water Ernst angles (, the flip angles for optimal SNR performance of fat and water protons. Although this angle is the point of highest SNR for fat fractions, using this flip angle generates considerably larger bias due to increased T 1 weighting. With precise knowledge of T 1, EQ 3 can be rewritten as EQ 4 to obtain proton densities of fat and water. A bias free fat fraction can then be determined using EQ 1. [4] T 1 mapping is not a standard part of in vivo scanning. The value itself is known to vary due to changes in the local environment [20]. However, it was demonstrated in simulations and phantom experiments that using an estimated T 1 will reduce difference between measured fat fraction and true fat fraction [15]. The bias reduction was evident even with the estimated T 1 being 46% different from the true T 1 [15]. While correction without proper T 1 mapping cannot remove the bias completely, it will allow fat fractions obtained at high flip angles to have similar bias compared to measurements obtained at low flip angles, while retaining improved SNR. This correction technique assumes accurate knowledge of flip angle used. However, this assumption can be invalid due to inhomogeneities of the RF pulses in MR systems of 3.0T and

above [21]. This RF inhomogeneity is a result of destructive interference of elements of the excitation coil, leading to nonuniform excitation across the slice, causing nonuniform flip angles across the slice. In a 3.0T system, RF inhomogeneities can cause the flip angle in a voxel to vary up to 50% from the prescribed value [18]. The effects of correction using erroneous flip angles can result in decreased bias reduction or in the worst cases actually introduce additional bias (FIG 3). By mapping the flip angle across the slice, the error due to flip angle will be reduced, minimising the amount of mathematical error in the process and thus improve the correction. FIG 3. Simulations of fat fraction with no correction, with bias correction only and with bias correction while fixing flip angle error. Imaging parameters were: T 1w =809ms, T 1f =343ms, TR=7.4ms. Prescribed flip angle was 12 o and true flip angle was 9 o. T 1 values used for correction were overestimated by 10%. It can be seen in FIG 3 that bias can be reduced further when T 1 estimation technique is coupled with flip angle mapping. With the T 1 estimation method, SNR performance can be optimized by acquiring signals using a flip angle between the Ernst angle of fat and water (e.g. 10 o ) while still retaining the low bias associated with the acquisition at a low flip angle. Thus, incorporating this T 1 bias correction with flip angle mapping would provide the least total error in an acquired fat fraction image. Methods and Materials Experiments were performed on 6 phantoms consisting of varying volume ratios of peanut oil and water, representing varying fat fraction levels [1.5%, 3%, 5%, 6%, 17%, 24%], and two phantoms of pure water and peanut oil. Peanut oil is used to represent fat due to its spectral peaks being almost identical to that of triglycerides, making it a good representation of in vivo lipids [22]. The true fat fraction of the phantoms were determined using single voxel Stimulated Echo Acquisition Mode (STEAM) spectroscopy with TE=30ms. Analysis of spectroscopy acquisitions were performed using analysis software with graphical interface utilizing known peak shapes as prior knowledge (fitman) [23]. Sample peaks were generated by using the spectrum obtained from the two pure sample phantoms. True fat fractions were determined by dividing the area under the fat peak with the combined area of the fat and water peaks. For validation of correction

effectiveness, fat fractions from measurements and corrections were compared to the true fat fraction. Phantoms were imaged at 3.0T (Discovery MR 750, GE Healthcare, Waukesha, WI) using a transmit-receive single channel quadrature head coil with an investigation version of the IDEAL- SPGR sequence at flip angle of 12 degrees. Image parameters were TR=7.7ms, TE=[1.5, 2.3, 3.1, 3.9, 4.7, 5.5] ms, echo-train length=2, Nx=256,Ny=256, FOV=24cm x 24cm, and slice thickness=5mm. Fat and water images were obtained by offline reconstruction using an IDEAL algorithm that corrects for T 2 * and B 0 inhomogeneities [24, 25]. Two more images were acquired with 5 and 29 degree flip angles so that the phantomt 1 s could be measured using DESPOT. A generalized flip angle map was obtained using the no inversion Double Angle Look-Locker method [18]. The same hardware as the IDEAL scan was used. Imaging parameters were TR=3ms, TE=155ms, TI=11ms, 64x64 matrix, FOV= 24cm x 24cm, slice thickness=5mm and 8 and 16 degree flip angles. A map of flip angle scaling factor k was obtained based on a flip angle map with prescribed flip angle of 8 degrees. The scaling factor, k, is, defined as: [5] Using the map of k, flip angle maps for each scan of different flip angles were generated as the product of k and the prescribed flip angle of the scan. T 1 bias corrections were performed on the phantom water and fat images to convert them to estimated proton density maps. T 1 estimates used were 350ms for water and 200ms for fat. These values were generated based on T 1 measurements in the phantoms (T 1w =274ms, T 1w =181ms) due to the T 1 of phantoms not corresponding to the values in vivo. Bias correction was performed using the algorithm outlined in FIG 4. Validation of correction effectiveness was performed by comparing the MRI acquired fat fraction with the fat fraction determined by spectroscopy.

FIG 4. Flow chart of bias correction algorithm. Bias correction is performed on a pixel by pixel basis on acquired fat and water images using flip angle measurements of the corresponding flip angle map. Fat fraction map is generated with bias corrected fat and water images. Results: The flip angle map of an acquisition with prescribed flip angle of 12 degrees is shown in FIG 5. It can be seen that the flip angle is homogeneously distributed (SD < 1%) with an average of 9 degrees per phantom. Compared to the prescribed flip angle, the in-slice true flip angle was 25 percent lower than expected. FIG 5. Flip angle map of phantoms imaged at prescribed flip angle of 12 o. Fat fraction of phantoms were: 100%, 17%, 6%, 1.5% for the first column; and 24%, 5%, 3% and 0% for the second column. The mean flip angle within phantoms was 9 o, 75% the value of the prescribed value. The distribution is homogeneous with little variation.

FIG 6. Fat fraction correction using T1 values of 350ms for water and 200ms for fat on the fat fraction map acquired at prescribed flip angle of 12 degrees. The phantom image on the left was corrected using flip angle map information, while the image on the right was corrected with the prescribed flip angle. It can be seen that that there is an overall decrease in fat fraction after correction. The reduction was greater for the image that used erroneous flip angle. FIG 6 shows a fat fraction difference map of the IDEAL fractions before and after correction, created by subtracting the uncorrected image from the corrected image. The pixel intensities in the difference maps are brighter in the difference map on the left (correction with flip angle mapping) than the right (correction map without flip angle mapping), indicating that bias correction using an overestimated flip angle results in a further reduction in fat fraction measurements, though not necessarily bringing the measurements closer to the true value. FIG 7. Fat fraction measurement of phantoms before correction, after T 1 correction only and after T 1 correction using flip angle map values. Not shown on the plot is the pure fat phantom. Measurements were (93% without correction, 91% with correction without flip angle map, 92% with correction with flip angle map). For fat fractions of above 5% shown on the plot, difference between measured fat fraction and true fat fraction was reduced when bias correction was applied, and reduced further when flip angle error was accounted for in the correction.

FIG 7 plots measured fat fraction measurement values against known true fat fraction values. It was observed that difference between true and measured fat fraction decreased by applying T 1 correction with or without incorporating flip angle mapping. Without accounting for flip angle mapping, bias was overcorrected, as can be seen from the measured fat fractions dropping below the line representing true fat fraction. While the introduction of flip angle mapping did not completely remove the bias, it can be seen that fat fraction measurements were brought closer to the true value if flip angle mapping was incorporated. For the 24% fat fraction phantom, bias was reduced from 3.5% to 1% by using T 1 correction, and was reduced to almost zero when flip angle error was corrected for. Discussion: The ability to accurately and precisely quantify fat fraction would be extremely useful in the monitoring and early detection of NAFLD. The difference between T 1 values of fat and water will confound the measured fat fraction. Although true T 1 measurements will not be obtained and will have small variations from pixel to pixel, performing T 1 correction with estimated T 1 values will bring measured fat fraction measurements closer to their true values, thereby increasing overall accuracy of measurements without any loss from changes in imaging parameters. For T 1 estimates in this experiment, T 1w was overestimated by 27% and T 1f was overestimated by 10%. It can be seen in FIG 7 that the difference between the fat fraction measurement and the true fat fraction was decreased after applying only T 1 correction and ignoring flip angle errors. Both our current and previous experiment [15] showed that using estimated T 1 values will reduce the amount of fat fraction bias, and thus obtain a more accurate fat fraction measurement while retaining the precision [15]. In this experiment, our flip angle map (FIG 5), showed that the prescribed flip angle was 25% larger true flip angles in the slice. Thus, the usage of an overestimated flip angle would result in over correction, as seen in FIG 6 and FIG 7. This was largely mitigated by using true flip angles measurements. For the correction, T 1 estimates were made after performing measurements. This was done because T 1 values in phantoms are shown to be significantly different from the in vivo measurements in our previous experiment [15, 20], and would lead to an unreasonable estimate if in vivo values were used. Performing T 1 measurements would not be possible for in vivo imaging due to the difficulty of performing flip angle mapping and multiple IDEAL acquisitions for DESPOT [17]. While it is true that a T 1 estimate that greatly differs from the true value will introduce more bias in the process, T 1 measurements obtained by de Bazelaire et al [20] were reported to be accurate with standard deviations of less than 10%. By using these values as references for corrections of in vivo acquisitions, estimated T 1 values are expected to be close to the true value. From FIG 6, it appears that the correction isn t effective at extreme fat fractions. To generate fat fraction maps, magnitudes of the signals are often used when calculating fat fraction to account for both magnitude and complex information due to unknown phase of fat and water signals [14]. By taking the magnitude of signals changes the noise, originally Gaussian with zero mean, to a Rayleigh distribution with a non-zero mean. This translates to bias at extremely low and high fat

fractions. There have been techniques proposed to counter this [14], but they were not employed in this experiment. The flip angle map obtained in this experiment showed uniform flip angle distribution with little variation. This result should not be expected in other scan sessions. Flip angle inhomogeneities are a result of non-uniform excitation RF pulse across the slice due to the RF pulse undergoing constructive interference with the subject being scanned. We used small phantoms for our experiments, so this effect was not as pronounced. However, with larger phantoms and in-vivo scans where the subjects are much larger the effect is more problematic. The effect of nonuniformity in RF pulse will be more of a problem as higher main magnetic fields are being employed, due to shorter RF wavelengths associated with higher magnetic fields. These factors increase the importance of flip angle mapping as part of the acquisition protocol [17, 21]. Conclusion: In this experiment, we have examined the effect of combining flip angle error correction via mapping and using T 1 estimates to correct for fat fraction bias. Compared to not correcting and correction without considering flip angle errors, bias correction using information obtained from a flip angle map was able to further reduce bias, as observed in FIG 7. This allows higher SNR performance by using higher flip angles. This suggests that bias correction combined with flip angle mapping should be incorporated into imaging protocols when quantifying fat fractions. The next step would be to validate this correction method on in vivo acquisitions and possibly performing this technique clinically for final validation. Acknowledgements: We thank Jacob Penner, Dr. John Drozd and Dr. Robert Bartha for their assistance in configuring and teaching us how to use fitman to analyze the spectrums of our phantoms. References: 1. Clark, J.M. (2006), The Epidemiology of Nonalcoholic Fatty Liver Disease in Adults, J Clin Gastroenterol, 40(1):5-10 2. Schwimmer, J.B., Deutsch, R., Kahen, T., Lavine, J.E., Stanley, C., & Behling, C. (2006), Prevalence of Fatty Liver in Children and Adolescents, Pediatrics, 118(4):1388-1393 3. Angulo, P. (2002) Nonalcoholic fatty liver disease, N Engl J Med, 346(16):1221-1231 4. Farrel, G.C., & Larter, C.Z. (2006), Nonalcoholic fatty liver disease: From steatosis to cirrhosis, Hepatology, 43(1):99-112 5. Yeh, M.M. & Brunt, E.M. (2007), Pathology of nonalcoholic fatty liver disease, Am J Clin Pathol, 128(5):837-847 6. Thampanitchawong P, Piratvisuth T. (1999) Liver biopsy: complications and risk factors.world J Gastroentero, 5(4):301-304, 27(5):1220-1226

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