 Research
 Open access
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Evaluation of B_{1} inhomogeneity effect on DCEMRI data analysis of brain tumor patients at 3T
Journal of Translational Medicine volumeÂ 15, ArticleÂ number:Â 242 (2017)
Abstract
Background
Dynamiccontrastenhanced (DCE) MRI data acquired using gradient echo based sequences is affected by errors in flip angle (FA) due to transmit B_{1} inhomogeneity (B_{1}inh). The purpose of the study was to evaluate the effect of B_{1}inh on quantitative analysis of DCEMRI data of human brain tumor patients and to evaluate the clinical significance of B_{1}inh correction of perfusion parameters (PPs) on tumor grading.
Methods
An MRI study was conducted on 35 glioma patients at 3T. The patients had histologically confirmed glioma with 23 highgrade (HG) and 12 lowgrade (LG). Data for B_{1}mapping, T_{1}mapping and DCEMRI were acquired. Relative B_{1} maps (B_{1rel}) were generated using the saturateddoubleangle method. T_{1}maps were computed using the variable flipangle method. Postprocessing was performed for conversion of signalâ€“intensity time (S(t)) curve to concentrationâ€“time (C(t)) curve followed by tracer kinetic analysis (K^{trans}, Ve, Vp, Kep) and first pass analysis (CBV, CBF) using the general tracerkinetic model. DCEMRI data was analyzed without and with B_{1}inh correction and errors in PPs were computed. Receiveroperatingcharacteristic (ROC) analysis was performed on HG and LG patients. Simulations were carried out to understand the effect of B_{1} inhomogeneity on DCEMRI data analysis in a systematic way. S(t) curves mimicking those in tumor tissue, were generated and FA errors were introduced followed by error analysis of PPs. Dependence of FAbased errors on the concentration of contrast agent and on the duration of DCEMRI data was also studied. Simulations were also done to obtain K^{trans} of glioma patients at different B_{1rel} values and see whether grading is affected or not.
Results
Current study shows that B_{1rel} value higher than nominal results in an overestimation of C(t) curves as well as derived PPs and vice versa. Moreover, at same B_{1rel} values, errors were large for larger values of C(t). Simulation results showed that grade of patients can change because of B_{1}inh.
Conclusions
B_{1}inh in the human brain at 3TMRI can introduce substantial errors in PPs derived from DCEMRI data that might affect the accuracy of tumor grading, particularly for border zone cases. These errors can be mitigated using B_{1}inh correction during DCEMRI data analysis.
Background
Dynamic contrastenhanced (DCE) MRI [1] is widely used for characterization and diagnosis of intracranial mass lesions [2]. A number of studies have shown the potential of DCEMRI in diagnosis and treatment of brain tumor [3,4,5,6]. DCEMRI has been in clinical and preclinical practice for more than two decades. Various mathematical models exist for analyzing DCEMRI data [1, 7,8,9,10,11,12,13]. Using the General Tracer Kinetic Model (GTKM) model [1], DCEMRI data can be used for extraction of various parameters viz. tracer kinetic parameters like volume transfer rate (K^{trans}), volume of extravascular extracellular space (Ve), plasma volume (Vp), as well as first pass analysis parameters like cerebral blood volume (CBV) and cerebral blood flow (CBF).
In general, DCE MRI data is acquired using fast Gradient Recalled Echo (GRE) sequences like SPGR/TFE. This makes the signal intensity of DCEMRI dependent upon FA. MRI images which are acquired using gradient echo based sequences are sensitive to B_{1} inhomogeneity at high field MRI scanner like 3T [14] up to 9T [15] depending upon RF coil and type of tissue used. This field inhomogeneity introduces flip angle (FA) related errors in signal intensity. Moreover, the FA errors can propagate to further quantitative analysis.
In a previously reported study [16] on breast tissue and simulated data, propagation of FA errors in DCEMRI data was investigated and it was reported that errors in K^{trans} and Ve vary nonlinearly with FA. Propagations of FA related errors to enhancement ratio, relative change between pre and post contrast, was previously reported for breast tissue [17]. Recently, another study on the effect of transmit B_{1} inhomogeneity on tracer kinetic analysis of DCEMRI data from breast cancer patients was also reported [18]. In this study effect of B_{1} inhomogeneity on precontrast T_{1} and kinetic parameters (K^{trans} and Ve) were reported. Propagations of FAbased errors on AIF estimations has also been reported for prostate tissue at 3T [19]. Thus there is a need for a systematic study using simulations and in vivo data, for evaluating propagation of errors on computed concentration and various perfusion parameters in the human brain.
Measurement of the T_{1} parameter is a prerequisite for DCEMRI analysis. A number of methods based upon inversion recovery [20, 21], Look locker [22], MOLLI [23], multiple Fast Spin Echo (FSE) image [24], and multiple FA [25, 26] are available for T_{1} estimation. T_{1} estimation based upon multiple FA is widely used due to shorter data acquisition time. However, T_{1} estimation using multiple FA based methods are sensitive to B_{1} field inhomogeneity [27,28,29]. In such cases, correction of T_{1} maps for B_{1} inhomogeneity is performed before further DCE MRI data analysis [30,31,32,33,34].
In the current study, in vivo DCEMRI data and B_{1} field map data from human brain tumor patients were acquired at 3T MRI to evaluate the effect of B_{1} inhomogeneity at different stages of DCEMRI analysis. Corrections for B_{1} inhomogeneity were applied during DCEMRI signal to concentration conversion. In addition, T_{1} map data was also acquired using multiple flip angles and corrected for B_{1} inhomogeneity. Simulations were performed to evaluate systematically the propagation of FA errors on DCEMRI data analysis. The clinical significance of B_{1} inhomogeneity was also investigated using statistical analysis and simulation studies.
Methods
Study population
The study protocol was preapproved by the Institutional Review Board of the Institute and all subjects provided written informed consent before MR scanning. The IRB Approval Number for this study is 2013001IP05. Thirtyfive patients (MaleÂ =Â 25, FemaleÂ =Â 10) having a mean age of 50.54Â Â±Â 15.36Â years (age range 16â€“77Â years) were recruited for the study. The patients had histologically confirmed glioma with 23 high grade (HG) [21 Grade IV and 2 Grade III] and 12 low grade (LG) [11 Grade II and 1 Grade I]. Grading was done as per World Health Organization guidelines.
MRI measurements
All MRI experiments were performed at 3T wholebody MRI system (Ingenia, Philips Healthcare, The Netherlands) using a 16 channel receive only coil. In this study, Multi Transmit parallel RF transmission was used to acquire MRI data. MRI protocol for this study included a triplane localizer acquiring conventional images for brain tumor patient, data for T_{1} maps, data for B_{1} maps and DCEMRI data.
For T_{1} mapping, 3D T_{1}W Turbo field echo (TFE) images were acquired with four FAs of 3Â°, 6Â°, 10Â° and 15Â°. Twelve slices, covering the tumor part, were acquired. Other MRI scan parameters were: slice thicknessÂ =Â 6Â mm; FOVÂ =Â 240Â Ã—Â 240Â mm^{2}; matrix sizeÂ =Â 256Â Ã—Â 256; TR/TE of 6.0/2.1Â ms.
MRI data for B_{1} map was also collected for all the subjects. Saturated dual angle method [30], with two FA interleaved approach, was used for B_{1} mapping. 2D TSE readout was used to acquire saturated dual angle images corresponding to 60Â° and 120Â°. FOV and number of slices were same as used in T_{1}W TFE images. TR/TE of 600/40Â ms was used to acquire images.
In the final step, DCE perfusion imaging was performed using a T_{1} Turbo field echo sequence (TR/TEÂ =Â 4.45/2.01Â ms; FAÂ =Â 10; slice thicknessÂ =Â 6Â mm; FOVÂ =Â 240Â Ã—Â 240Â mm^{2}; matrix sizeÂ =Â 256Â Ã—Â 256). At the fourth time point of the 3DDCEMRI data acquisition, 0.1Â mmol/kg body weight of gadobenate dimeglumine GdBOPTA (Multihance, Bracco) was administered intravenously with the help of a power injector at a rate of 3.0Â ml/s, followed by a bolus injection of a 30ml saline flush [11]. A series of 384 images, 32 time points for 12 slices, were acquired with a temporal resolution of 3.9Â s.
Quantification of perfusion parameters
In the current study, DCEMRI data analysis involved following steps:
B_{1} mapping
The B_{1} map was generated using saturated double angle based method [30]. Two images are acquired: I1 and I2 such that the tip angle of I2 is twice of I1. All other signalaffecting sequence parameters are kept constant. If the effects of T_{1} and T_{2} relaxation can be neglected, then it can be shown that
Here \(\theta\) corresponds to the tip angle that vary with the spatially varying B_{1} field. I_{1} and I_{2} corresponds to images obtained at FA 60Â° and 120Â° respectively. Computed angle \(\theta\) was divided by angle of 60Â° degree to generate relative B_{1} (B_{1rel}) map. True or nominal value corresponds to B_{1rel}Â =Â 1.
Mean (Â±SD) value of B_{1rel} map for all slices of 35 patients were computed and plotted. This has been done on both entire brain region covering all slices and on entire tumor region of a particular slice to estimate the B_{1} inhomogeneity range among these patients.
Estimation of T_{1}
T_{1} map was computed using previously reported multiple FA based method [35]. The FAs used in the current study were 3Â°, 6Â°, 10Â° and 15Â°. T_{1} maps using multiple FA based method were generated by fitting the pixelwise image intensities of the abovementioned FAs to Eq. (2) (described in the next section) using a nonlinear leastsquare fitting routine in MATLAB. The â€˜lsqcurvefitâ€™ routine in MATLAB with lower and upper bound of 200 and 5000Â ms and an initial guess of 1000Â ms was used for curve fitting. The lsqcurvefit routine uses the trustregionreflective algorithm. For obtaining B_{1} inhomogeneity corrected T_{1} map, all FAs were corrected pixelwise for B_{1} inhomogeneity using B_{1rel} map [30].
Effect of B_{1} inhomogeneity on DCEMRI data and its corrections
Signal intensity for SPGR/TFE signal is represented by the following equation:
where \(M_{0}\) is the equilibrium longitudinal magnetization. \(M_{0}\) is given as \(G\). \(\rho\) where \(G\) is the gain and \(\rho\) is the proton density. TR and TE represents repetition and echo times, T_{1} and T ^{*}_{2} are relaxation times and \(\theta\) is the FA.
The signal S is a function of Î¸. Therefore, DCE MRI data which is acquired before, during and after intravenous injection of contrast agent show dependence on FA. B_{1} field inhomogeneity results in variation of nominal FA and hence in the signal intensity time curve (S(t)) of DCEMRI data. These variations propagate to further DCEMRI analysis. Due to B_{1} inhomogeneity, voxelwise FA (at ith voxel) is given by the following equation:
Here \(\theta (i)\) is the modified FA at ith voxel, according to B_{1rel} value at corresponding voxel, and \(\theta_{nominal}\) is the nominal value specified by user in MRI protocol. Since, data provided by scanner at a voxel (i) correspond to Î¸(i) given by Eq.Â (3) therefore, during quantitative analysis, Î¸(i) should be used instead of \(\theta_{nominal}\) in order to remove the effect of B_{1} field inhomogeneity.
Since we are mainly interested in quantitative analysis of DCEMRI data and the first step is the conversion of S(t) toC(t), therefore, itâ€™s important to correct C(t) for B_{1} inhomogeneity. In this study, S(t) was converted to C(t) using previously described procedure [24].
Contrast agent changes the relaxation rates of tissues. The increase in relaxation rates are linearly related to contrast concentration in the tissue:
Here r1Â =Â 5.9Â l/mmol/s and r2Â =Â 17.5Â l/mmol/s at 37Â Â°C and 3T [36]. After injection of contrast, the signal from an SPGR sequence is given by [24]:
For this particular study, TE is small enough to neglect its effect. Briefly, the above equation can be reduced to
where \({{K_{0} = (1  \cos (\theta ) \cdot e^{{(  TR/T_{10} )}} )} \mathord{\left/ {\vphantom {{K_{0} = (1  \cos (\theta ) \cdot e^{{(  TR/T_{10} )}} )} {(1  e^{{(  TR/T_{10} )}} )}}} \right. \kern0pt} {(1  e^{{(  TR/T_{10} )}} )}}\), \(E3 = e^{{\left( {  TR.\left( {\frac{1}{{T_{10} }} + r1 \cdot C(t)} \right)} \right)}}\).
T_{10} is the value of T_{1} of tissues before injection of contrast agent. C(t) is the concentration of GdBOPTA at time â€˜tâ€™ in the tissue and C(0)Â =Â 0. Since in this study, T_{10} is estimated separately, therefore, Eq.Â (6) is a nonlinear equation with only 1 unknown parameter C(t). This equation was solved to obtain the value of C(t) at different time points.
While converting S(t) to C(t), voxelwise FA as given by Eq.Â (3) was used. Here only precontrast T_{1} values (T_{10}) are required as opposed to T_{1}(t) at each time point during direct correction of S(t). This step resulted in B_{1} inhomogeneity corrected C(t) curves. For generating C(t) without B_{1} inhomogeneity correction, we used \(\theta_{\text{nominal}}\) as the \(\theta\) in Eq.Â (6).
Estimation of AIF
In this study, we have used automatically detected local arterial input function (AIF) for each glioma patient using previously described procedure [10]. Briefly, the method for automatic extraction of AIF is based on the features exhibited by the concentrationâ€“time curve in vascular voxels. The main features of concentrationâ€“time curve at arterial voxels are: early arrival of contrast or early bolus arrival time, high peak value (during first pass), early arrival of time to peak; sharp uptake (high gradient value) of contrast agent, and high average value of concentration of contrast.
Tracer kinetic model fitting
In the current study we have used generalized tracer kinetic model (GTKM) described previously [1] for estimating kinetic parameters particularly volume transfer rate (K^{trans}), volume of extracellular extravascular space (Ve), plasma volume (Vp) and Kep which is the ratio of K^{trans} and Ve. Briefly, following equation of GTKM is used:
where C_{T} is the concentration of contrast in tissue/voxel and Cp is AIF. Voxelwise fitting of GTKM was performed using inhouse written programs in MATLAB and inbuilt MATLAB routine function â€˜lsqcurvefitâ€™ which uses the trustregionreflective algorithm. The upper bound and lower bound values for K^{trans}, Kep and Vp was [1, 2, 8] and [0, 0, 0]. Ve was estimated as the ratio of K^{trans} and Kep. Tracer kinetic model fitting followed the previously described procedure [24].
First pass analysis
First pass analysis [37] for estimation of hemodynamic maps of CBF, CBV and corrected CBV (CBV_Corr) were carried out using previously described procedure [24]. It needs to be mentioned here that there is an overestimation of CBV in the regions where the contrast leaks into extravascular extracellular space because in this case, it represents the volume of contrast in intravascular as well as in leakage space. CBV_Corr represents the volume of blood only in the intravascular space and is to be estimated by removing the contribution of fractional leakage space volume (Ve) from the CBV.
Sample size estimation
To evaluate the clinical significance of B_{1} inhomogeneity statistical analysis was performed. The sensitivity and specificity of the perfusion parameters were calculated using receiveroperating characteristic (ROC) analysis. To estimate the sample size required for differentiation between HG and LG patients, it was assumed that the area under the ROC curve (AUC) of 0.8 is significant from the null hypothesis value 0.5 (meaning no discriminating power). For 95% power and a 0.1 level of significance, the minimum sample size required for positive (HG) and negative responses (LG) was 22 and 11 respectively. A total of 23 high grade (HG) which is Grade4 and Grade3 combined and 12 low grade (LG) which is Grade2 and Grade1 combined, patients were taken for this study.
Statistical analysis
Within the tumor region of a particular slice, 2â€“3 circular regions of 5 voxel radius showing high values of post B_{1} corrected CBV_Corr were manually placed and the one showing maximum value was chosen as Region of Interest (ROI). All perfusion parameters before B_{1} correction and after B_{1} correction were obtained from the ROIs. Relative percentage error (RPE) for with and without B_{1} inhomogeneity correction, were computed for C(t) and perfusion parameters corresponding to these ROIs. RPE was defined as:
These perfusion parameters were further used for ROC analysis. Cutoff value at which the average of sensitivity and specificity is maximized and area under the curve of ROC analysis were obtained for grading between HG and LG gliomas. Histologically confirmed grades were taken as a gold standard. All analysis was done using SPSS statistics software package version 16.0. A paired t test with twotailed distribution was done to find out whether the change in each perfusion parameter before and after B_{1}Â correction is significant or not. The Blandâ€“Altman (BA) plot was also computed to compare values of perfusion parameters before and after B_{1} correction. In this graphical method, the differences between the two techniques are plotted against the averages of the two techniques. Here the difference of parameters is plotted against postB_{1} correction technique since that is the reference method. The mean difference should be less than the limits of agreement which is defined as the 95% CI of the mean difference, for the agreement between results of with and without correction.
Simulations
Simulations were carried out to understand the effect of B_{1} inhomogeneity on DCEMRI data analysis in a systematic way. EquationÂ (6) was used for simulating S(t) curves mimicking those in tumor tissues. Parameters used in the simulation are shown in TableÂ 1. For simulated AIF we have used parameters as reported in the literature [38]. Three cases were simulated in this study. In the 1st case, C(t) values from 0:0.01:0.5Â mmol/l were used to generate S(t) curve using Eq.Â (6). Now while converting back from S(t) to C(t), errors in FA were introduced for mimicking B_{1} field inhomogeneity effect. This was done to understand the effect of initial concentration amount on an error in C(t) due to different B_{1} inhomogeneity errors. In the 2nd case, C(t) curves mimicking response of tumor tissue were generated without and with different B_{1} inhomogeneity errors. This was done to evaluate the error in C(t) due to B_{1} inhomogeneity. In 3rd case, three C(t) curves having different concentration amounts (mimicking those in tumor tissue) were generated and effect of B_{1} inhomogeneity errors in various parameters were computed. This involved using different K^{trans} values [0.1, 0.2, 0.3] as the starting values to generate three different C(t) while keeping Kep and Vp valuesÂ fixed as shown in TableÂ 1. The goal of this study was to estimate the change in perfusion parameters as a result of change in C(t) curves due to FA error. It needs to be mentioned that in simulation studies the FA for dynamic study is 10Â° which is same as the FA used in in vivo data.
Another simulation study was done to illustrate the clinical significance of B_{1} inhomogeneity correction. 5 HG (Grade3 and Grade4) and 5 LG (Grade1 and Grade2) patients were randomly selected. K^{trans} values after B_{1} correction corresponding to the chosen ROI were used. B_{1rel} was altered from a range of 0.75â€“1.25 to see how it influences the perfusion parameters. The C(t) values were kept same for all of them to study the influence of B_{1} exclusively on perfusion parameters. The threshold for grading used in this study was same as that obtained from ROC analysis after B_{1} correction.
Results
In the current study, it was evident that B_{1} inhomogeneity was present across different MRI image slices of human brain. FigureÂ 1 shows B_{1rel} maps of multiple brain slices of one subject. B_{1rel} values were higher than the nominal value of 1 in the central part of the brain. In the peripheral region of the brain, B_{1rel} values are found to be less than the nominal value of 1.
Histogram plot of B_{1rel} values for 12 brain slices of a particular patient in Fig.Â 2a shows a broad distribution of B_{1rel} values which extends to both sides of the nominal value. For this subject, B_{1rel} values range in the brain slices were [0.85â€“1.25] with the maximum value found between 1 and 1.05. FigureÂ 2b, c show plots of B_{1rel} values (meanÂ Â±Â SD) of the entire brain and tumor tissue respectively for 35 different subjects. Large variations in B_{1rel} values of entire brain was observed in each of 35 patients. More importantly, it was observed that meanÂ B_{1rel} values ranged from 3% below nominal to 20% above nominal in the tumor region among different patients.
TableÂ 2 shows B_{1rel} values and corresponding relative percentage error (average valueÂ Â±Â S.D) of different parameters at the previously mentioned ROI in tumor region for 35 different patients. B_{1rel} values ranging from 0.95 to 1.25 at an interval of 0.05 has been shown. RPE of all perfusion parameters shows an increasing trend with an increase of B_{1rel} values. For B_{1rel} values less than the nominal range (which is equal to 1), RPE of perfusion parameters is negative and vice versa. Kepâ€™s values are not presented in the table as it is not an independent parameter, being the ratio of K^{trans} and Ve.
FigureÂ 3 show data from a patient with glioblastoma (GBM) having a B_{1rel} value of 1.15 in an ROI in the tumor region pointed by the arrow. An enhancing ring like tumor region is visible in that slice. In the ROI a steep rise in concentration was observed because of contrast leakage into the tumor due to the Blood Brain Barrier breakdown. In Fig.Â 3b B_{1rel} map shows the inhomogeneous B_{1} distribution in the particular slice of brain. FigureÂ 3c shows that C(t) at the tumor location reduces after B_{1} inhomogeneity correction over 32 time points. FigureÂ 3d shows that there is a relative percentage error of 11.65% in concentration at the end of 32 time points. Bolus arrival time for this ROI was at the 8th time point. Therefore, first 7 time points were excluded from error computation. FigureÂ 3e shows the relative percentage error in various perfusion parameters due to B_{1} inhomogeneity. It shows that a B_{1rel} value greater than nominal value (before correction) results in an overestimation of parameters CBV, CBVCorr, CBF, K^{trans}, Ve, Vp. For this subject, Ve showed maximum RPE of ~Â 16%.
FigureÂ 4 shows data from a subject with brain tumor having a B_{1rel} value of 0.94 (lower than nominal value) in the tumor region. FigureÂ 4a shows the tumor location in the postcontrast T_{1}W image. FigureÂ 4b shows that the B_{1rel} value in the ROI taken from tumor region is below the nominal value. FigureÂ 4c shows the C(t) at the tumor ROI is increased after B_{1} Correction. FigureÂ 4d shows that there is a relative percentage error of 6.3% in concentration at the end of 32 time points. Bolus arrival time for this ROI was around 9th time point. Therefore, first 8 time points were excluded from error computation. The lower value of B_{1rel} results in an underestimation of C(t), which was corrected after B_{1} inhomogeneity correction. Similarly, all perfusion parameters, show underestimation with a relative percentage error of K^{trans} reaching âˆ’Â 6.3% shown by in Fig.Â 4e.
TableÂ 3 gives relative % change in variation (calculated as square of SD) of each perfusion parameter for both HG and LG patients. Mostly, it was seen that variation of perfusion parameters reduced after correction within each grade.
Dependence of FA related errors, using simulations, in computed concentration on the amount of nominal concentration is shown in Fig.Â 5. It was observed that FA related errors increase with an increase in the amount of concentration. FigureÂ 6 show propagation of B_{1rel} errorsÂ to simulated C(t). Simulated C(t) curve mimics those of contrast enhancing tumor region. Simulations show thatÂ values of B_{1rel} lower than nominal value results in an underestimation of C(t) while higher values result in overestimation. This behavior was similar to experimental results obtained from brain tumor patients.
Simulation results shown in Fig.Â 7 demonstrate the dependence of B_{1} inhomogeneity related errors in perfusion parameters on the concentration of contrast agent. Overall, errors in all the parameters increased with increase in the concentration of contrast agent. Parameter Ve showed the maximum error.
FigureÂ 8a shows that the cutoff for K^{trans} between HG and LG patients is 0.77. Patient 2, 8, 10 were HG and remained HG at different B_{1rel} values. Patient 1, 5, 7 were LG and remained LG with a change in B_{1rel} values. Patient 4 changed from HG to LG at B_{1rel} less than 8, patient 3 changed from HG to LG at a B_{1} value less than 0.95, patient 6 changed from LG to HG at B_{1rel} greater than 1.15 whereas patient 9â€²s grade changed from LG to HG at the B_{1rel} value of 1.25 or more. FigureÂ 8b shows the same graph for borderline patients 3, 4, 6 and 9 for better visualization.
Paired t test result showed that changes in each perfusion parameter before and after correction is significantly different (pÂ <Â 0.001). In Fig.Â 9 Blandâ€“Altman plots for perfusion parameters showed that for each parameter the mean difference fell within the limits of agreement for the majority of subjects. However, for all metrics, two to three subjects fell outside the limits of CI.
Discussion
In the current study, B_{1} inhomogeneity in the human brain with tumor at 3T MRI was estimated and its effect on concentrationâ€“time curves and derived perfusion parameters was evaluated using experimental as well as simulated data. Mean B_{1rel} ranged from 3% below nominal to 20% above nominal in tumor tissues of different patients, which resulted in erroneous estimates of concentrations as well as perfusion parameters. It was also observed that B_{1rel} in tumor ROI is lower than nominal for few patients whereas it was higher than nominal for the majority of patients. This resulted from the heterogeneous B_{1rel} field across the brain. Centre of the brain shows B_{1rel} values much higher than nominal compared to the periphery. Thus tumor near the central part of the brain had higher B_{1rel} values compared to a tumor in the periphery region. Simulation results provided a systematic evaluation of propagation of FA related errors in DCEMRI data analysis. The current study shows that B_{1rel} value greater than nominal results in overestimation of C(t) curves as well as derived perfusion parameters. Similarly, B_{1rel} values lower than nominal result in underestimation of parameters. Kep being a ratio of K^{trans} and Ve didnâ€™t provide any unique information and hence was not mentioned in the results. Preliminary results of this study have been reported [39].
One of the observations in the current study was that errors in C(t) due to B_{1} inhomogeneity increases non linearly with increase in concentration amount. The amount of concentration in contrast enhancing tumor region is different for different patients. The errors in perfusion parameters have a complex dependence on the amount of concentration and B_{1rel} value at a particular ROI.
In the current study, a 2D TSE readout technique was used to acquire B_{1} map data. This technique is intrinsical to slice selection because of slice selective refocusing pulses. So, a nonselective excitation pulse (at 2 different angles) can be used without having to go for a 3D volume acquisition. Thus the used sequence provides fast and accurate results without taking into account the slice profile of excitation pulse. Moreover, during dynamic image acquisition, an echo time of 2.1Â ms was used. It was seen through some preliminary studies that changes in T_{20} at such a small TE didnâ€™t affect the calculation of DCE parameters. Thus in this study, we have neglected the effect of T_{20}.
In the current study, lower and upper bound values during T_{1} map estimation and Tracer kinetic model fitting using Matlab routines were decided based on physiological constraints of a particular tissue.
The first step in DCE MRI analysis requires precontrast T_{10} map calculation. In the current study, T_{1} estimation was performed using multiflip angles. The T1 map obtained was found to be effected by B_{1} inhomogeneity. Hence, T_{1} map was also corrected for B_{1} field inhomogeneity. In the current study, relative percentage error (RPE) of DCE parameters were positive for B_{1rel} values greater than 1 and negative for B_{1rel} values less than 1. This trend is opposite to the findings of Bedair et al. [18]. This is because, in the current study, RPE is calculated with respect to results of post B_{1} correction, which is the corrected value.
There is a monotonic increase in RPE of all DCE parameters although not linearly. This is because of the different concentration amount reaching the tumor in each patient and it has been shown in simulation studies that amount of concentration reaching the tumor also plays a role in deciding RPE of perfusion parameters.
It should be mentioned here that 3D acquisition of DCE MRI data can result in inhomogeneous slab selection. However in the current study, tumor from central slice has been chosen in which inhomogeneous slab selection is not a problem.
The simulation studies have been designed to evaluate FA related error propagations in a systematic way and to verify the experimental results. Simulation studies helped in covering a wide range of concentration and B_{1} inhomogeneity, which was difficult to cover using experimental data of the current study. Moreover, experimental data results can be affected by noise, which might influence the true behavior of error propagation. Without simulations, itâ€™s difficult to demonstrate that B_{1} inhomogeneity errors depend both on B_{1rel} value and initial contrast agent concentration. In the simulation study a T_{1}Â =Â 1500Â ms, which is similar to that of enhancing tumor tissue was used to obtain the results. It was found that similar results were obtained for different T_{1} values such as 800, 1200 and 2000Â ms (results not shown). In the current study, local AIF obtained from each patient data was used for DCEMRI analysis. However, for simulation studies, global AIF was used. Global AIF can be obtained as an average of local AIFs from different patient data or based on published literature.
It can also be intuitively seen that cut off values for differentiating between grades will be always dependent on tumor location and B_{1rel} value at that ROI. Since, this will be changing from patient to patient, cut off values will also be varying arbitrarily as more and more patients are added to the study. This problem wonâ€™t arise if B_{1} correction is conducted beforehand. Thus the clinical significance of using B_{1} correction is intuitionally evident.
In a limited in vivo data set, it is not always possible to get appropriate cases where B_{1} correction can come into clinical importance. Appropriate cases are those where high B_{1} inhomogeneity coincides with ROI (obtained from the maximum CBV_Corr region) within the tumor of glioma patients. This may not happen in many glioma patients and can purely depend on chance depending on tumor ROI location and B_{1} inhomogeneity of that ROI. Thus Blandâ€“Altman plots showed that the mean difference between before and after B_{1} corrected perfusion parameters were outside the limits of agreement for few subjects. However, a number of cases were border zone cases. In the current study, the sensitivity, specificity, and AUC of perfusion parameters from ROC analysis did not show much change between pre and post B_{1} correction to come to any conclusive decisions (results shown in Additional file 1). Hence, simulations were performed using in vivo data to demonstrate the effect of B_{1} inhomogeneity correction on the accuracy of grading. K^{trans} was chosen for simulation studies as it had maximum AUC as was found from ROC analysis (Additional file 1). It needs to be mentioned here that cutoff value of K^{trans} used in simulation studiesÂ was from B_{1} corrected results. Change in grade has been observed in those cases where the deviation of the value of the grading parameters from cutoff value is less. This suggests that B_{1} inhomogeneity may influence glioma grading in cases where perfusion parameter values are on the borderline of cut off value for separating highgrade from lowgrade glioma.
It was also observed from TableÂ 3 that for both HG and LG patients, intragroup variation of perfusion parameters reduced after B_{1} correction even with a small sample size. This observation highlights the importance of B_{1} correction when perfusion parameters are used for clinical diagnosis such as grading.
In this study, the FA used for obtaining DCEMRI data is 10 degree, which is around two times compared to Ernst angle corresponding to TR of 4.45Â ms. The nature of error propagated to DCEMRI data can also vary depending on the FA used. For a fixed TR, B_{1} related errors on dynamic data analysis reduce with increase in FA compared to Ernst angle (observation based on simulation, result not shown). However, this also results in a reduction of SNR in DCEMRI data. Therefore, a tradeoff is usually carried out during protocol designing to select appropriate FA for a fixed TR. On the other hand, B_{1} inhomogeneity correction enables to use DCEMRI data corresponding to FA close to Ernst angle and hence obtain an improved SNR.
One of theÂ limitation is the unavailability of enough patient data so as to illustrate the clinical significance of this study. However, this limitation was addressed by using simulation using in vivo study results. In this study, ROI selection was done on the basis of maximum CBV_Corr values in the tumor region. However, for accurate selection of ROI, those regions should be avoided where high CBV_Corr values coincide with blood vessels. In the current study, we have used SDA based approach for B_{1} mapping. There are many alternative sequences which can be used for B_{1} mapping. A detailed study needs to be done to investigate how the FA related errors in the quantitative analysis of DCEMRI data varies with different B_{1} mapping approaches. Another future work in this study is to optimize the FA used for obtaining DCEMRI data based on B_{1} inhomogeneity propagated error.
B_{1} field inhomogeneity depends upon MRI scanner field strength, type of coil as well as the type of tissue being studied. A recently reported study on breast DCEMRI showed an average of 37% FA difference between the right and left breast [18]. B_{1} field inhomogeneity increases with increase in MR scanner field strength. For example at 7T, reported studies have shown B_{1} field inhomogeneity of ~Â 50% in human brain data [33]. Such a large B_{1} field inhomogeneity can result in proportional variations in FA, which can lead to errors in DCEMRI data analysis at 7T. In the current study we have demonstrated results for brain data at 3T; however, similar results should be observed for DCEMRI studies of different organs as well as at ultrahigh field scanner 7T.
Conclusions
In conclusion, a substantial transmit B_{1} field inhomogeneity was observed in tumor tissues of the human brain at 3T MRI scanner. It was demonstrated that it can introduce errors in the quantitative parameters derived from DCEMRI data, which can affect diagnosis and prognosis of patients. B_{1} inhomogeneity related errors in the DCEMRI analysis showed dependence on B_{1rel} values, contrast agent concentration as well as on the length of DCEMRI data. Overall, B_{1} inhomogeneity results in erroneous estimates of quantitative parameters. Correction of FA errors during conversion of S(t) to C(t) can mitigate these errors and provide an improved diagnosis.
Abbreviations
 B_{1rel} :

relative B1
 S(t):

signal time curve
 C(t):

concentration time curve
 FA:

flip angle
 RPE:

relative percentage error
 HG:

high grade
 LG:

low grade
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Authorsâ€™ contributions
ASe and ASi were involved in protocol/project development, data collection, data analysis and manuscript writing while RKG was involved in protocol/project development, data management, clinical inputs and manuscript editing. All authors read and approved the final manuscript.
Acknowledgements
The authors acknowledge the technical support of Philips India Limited in MRI data acquisition. The authors thank Mr. Rakshit for image processing; Dr. Indrajit Saha, Dr. Prativa Sahoo, Ms. Rupsa and Mr. Karthick for technical assistance; Dr. Pradeep Kumar Gupta for data handling.
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The authors declare that they have no competing interests.
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The data sets used and/or analyzed during the current study are available from the corresponding author on request.
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All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. Informed consent was obtained from all individual participants included in the study.
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Authors acknowledge the funding support from Science and Engineering Research Board (SERB) (Grant Number: YSS/2014/000092) and internal grant from Indian Institute of Technology Delhi.
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Sengupta, A., Gupta, R.K. & Singh, A. Evaluation of B_{1} inhomogeneity effect on DCEMRI data analysis of brain tumor patients at 3T. J Transl Med 15, 242 (2017). https://doi.org/10.1186/s1296701713497
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DOI: https://doi.org/10.1186/s1296701713497