Effect of different number of diffusion gradients on dispersion degree of FA values and its SNR Na Zhang1,2 Zhensheng Deng1*Xiaojuan Yin1 1.Institute of Biomedical Engineering,School of Info-physics and Geomatics Engineering,Central South University,Changsha,China Xin Liu2 Hairong Zheng2*2.Paul C.Lauterbur Research Centre for Biomedical Imaging,Institute of Biomedical and Health Engineering,Shenzhen Institutes of Advanced Technology,Chinese Academy of Science,Shenzhen,China corresponding author:*first:Zhensheng Deng()*secondary:Hairong Zheng()AbstractTo study the effect of different number of diffusion gradient directions(NDGD)of diffusion tensor imaging(DTI)on dispersion degree of fractional anisotropy(FA)values and its signal noise ratio(SNR)for adult brain tissues.Eight health volunteers were imaged by a 1.5T magnetic resonance scanner with different NDGD(6,9,12,15,20,25,and 30 noncollinear)respectively,and seven FA maps associated with the different NDGD were obtained.Four region of interest(ROI)(genu and splenial of corpus callosum,genu and posterior limb of internal capsule)were chose in white matter of FA maps,and FA values and its SNR of the ROIs were computed and compared.Analysis of variance and independent-samples t-test were performed with a p value less than 0.05 regarded as statistical significance.Variance of FA values within the ROIs with stronger signals(genu and splenial of corpus callosum)fluctuated randomly and had no linear relationship with NDGD,and SNR increased slightly with NDGD increasing.But variance of FA values within the ROIs with weaker signals(genu and posterior limb of internal capsule)diminished significantly with NDGD increasing from 6 to 20,and slowly in the range from 20 to 30.SNR of FA values within the ROIs with weaker signals was improved significantly with NDGD increasing from 6 to 20(P0.05).To detect FA values and its fluctuation and SNR of the ROIs with stronger signals,NDGD=6 is enough.for detecting those of the ROIs with weaker signals,however,considering that reducing of scanning time to lower possibility of movement-derived artifact and increasing of NDGD to improve precision of FA values,NDGD=20 is an optimal choice.Keywords-Diffusion Tensor Imaging;Number of Diffusion Gradient Directions;Fractional Anisotropy;Variance;Signal Noise Ratio I.INTRODUCTION Diffusion tensor imaging(DTI)can be used to analyze quantificationally the characteristics of movement of water molecules,and provide the information of earlier lesion 1 that the routine magnetic resonance image(MRI)can not.It is a non-invasive exciting new technique for assessment in vivo of white matter structural integrity and connectivity in human brain.The diffusion of water molecules in brain tissues is significantly hindered by the presence of cell membranes,myelin sheaths surrounding axons,and other structures.Hence,the diffusive movements are different in different directions,that is,the movement can be stronger in one direction,and weaker in another one.This direction-dependent diffusive movement is called anisotropic diffusion 2.The anisotropic diffusion can be described mathematically as a tensor which contains information about both the direction and the magnitude of restriction.It is generally agreed that the diffusion tensor can be modeled by a 3 dimension(3D)ellipsoid in each voxel.With the diffusion tensor,three dimensional shape and diffusion magnitude of water motion within the brain can be measured 3,and then some quantitative measurements can be calculated and mapped,such as fractional anisotropy(FA),which describes the degree of diffusion anisotropy of water molecule 4.Number of diffusion gradient directions(NDGD)is one of the key parameters in the acquisition of diffusion weighted(DW)images.To calculate diffusion tensor D,a minimum 6 DW images with different diffusion gradient directions should be acquaired for each slice in DTI,i.e.NDGD is equal to 6.Generally speaking,with the NDGD increasing,more DW images are used to calculate diffusion tensor,a much preciser estimation for tensor will be acquired 5.But with the NDGD increasing,scanning time needed for acquiring images become much longer,which not only impropriates too much resources of MR equipment,makes patient uncomfortable,but also increases greatly the probability of movement-derived artifact due to much longer imaging time,which degrades the quality of DW images.Therefore,it is still in question that how many NDGD can ensure a precise estimation of tensor 510.Some researchers 6 investigated the effect of NDGD on FA value and its SNR under the condition of constant image acquisition time.But with the NDGD increasing,the number of images collected corresponding to each diffusion gradient direction will be less because of the constant image acquisition time.So the number of images averaged will also be less and the SNR is poorer.In a similar way,more DTI images can be collected for one slice with the NDGD decreasing,thus the SNR of image will be improved with the number of excitations(NEX)increasing.Therefore,it is difficult to distinguish that the reason of instability of FA values is due to the SNR of the original images or NDGD.Others 5 researched the effect of NDGD on FA values and SNR with the fixed NEX.The advantage is that it can maintain the original SNR of images constant,and the 978-1-4244-4713-8/10/$25.00 2010 IEEEfluctuation of FA values only is dependent on NDGD.But they didnt investigate the effect of inherent signal intensity within the ROIs on FA values and its fluctuation.To study the effect of different inherent signal intensity within selected ROIs on FA values and its SNR,the NEX is fixed in this paper so as to all the 7 different NDGD have the same original SNR,then four ROIs which are genu and spenium of corpus callosum(Gcc,Scc),genu and posterior limb of internal capsule(Gic,Plic)with different inherent signal intensity in white matter are chose in order to compare the effect of NDGD on dispersion degree of FA values and SNR,and study whether the inherent signal intensity within selected ROI impacts on the FA values and its fluctuation.II.MATERIALS AND METHODS A.Subjects All DTI data used in this paper are identical with the literature reported by Na Zhang et al 5,i.e.eight health adult volunteers(five males,and three females;range,21-29)participated in the study.None of participants had any history of neurological diseases.Institutional review board approval was obtained for the study,and all subjects gave informed consent.All images were downloaded from the website of Johns Hopkins Medical Institute Laboratory of Brain Anatomical MRI with permission.B.Data Acquisition Equipment and Imaging Parameters According to the literature reported by Hangyi Jiang 10,all DTI images was acquired on a 1.5T MR scanner(Gyroscan NT;Philips Medical Systems,Best,the Netherlands).By using a single-shot echo-planar imaging sequence,all DTI data acquisitions were performed with 7 different NDGD(6,9,12,15,20,25,and 30 noncollinear),and b=700s/mm2.At the same time,for each slice,five additional images with minimal DW(b_0=33 s/mm2)were also acquired,and all DTI data have the same b_0 images.Parameters for DTI data are as follows:matrix=256 256,Field of View(FOV)=246 220 mm,and the thickness of the transverse sections is 2.2 mm,which are parallel to the anterior commissureposterior commissure line.The scan covered the entire hemisphere and brainstem without gaps,and totally 55 sections were acquired in about six minutes.To make all the images have the same original SNR,all DW imaging were repeated three times.C.Acquisition of FA Maps According to previous researcher 11,three eigenvalues,1,2,3 from the diffusion tensor,which represent the magnitude of diffusivity in the three directions,can be determined by diagonalizing the tensor for each voxel.Based on these three diffusivities,the FA which describes anisotropy degree of water diffusion is calculated to yield values between 0 and 1 by the following Equation,as in(1):()()()23222123222123+=FA (1)Where,3321+=The DW images are processed by employing DTI Studio 11,which can be used for diffusion tensor calculating and fiber tracking.The FA maps from one subject in the 7 different NDGD are shown in Figure 1.Figure 1.The FA maps from the 7 different NDGD corresponding to 6,9,12,15,20,25,and 30 noncollinear,which arranged in turn from upper left to lower right,from which the improvement of the SNR with the NDGD increasing could be observed visually.D.ROI Selection and SNR Calculation In order to illustrate the effect of NDGD on dispersion degree of FA value and its SNR in different region of brain,and to make the results more common,FA values and its SNR of four ROIs(Gcc,Scc,Gic,and Plic)selected on white matter of FA maps associated with 7 different NDGD were calculated respectively based on Matlab platform.The SNR of a ROI is estimated approximately by the ratio of the mean intensity of FA within ROI to the minimum of the local standard deviation outside the ROI.As shown in Figure 2,it is an FA map with NDGD=30,and four selected ROIs.It can be seen Obviously that the signals of the ROIs in Gcc and Scc are stronger than those of the ROIs in Gic and Plic.Figure 2.An FA map corresponding to 30 noncollinear diffusion gradient directions,with four ROIs(about 30 pixels)in the white matter marked with red circles.gcc,gic,plic,scc E.Data Analysis Software of SPSS11.5 was employed to perform statistical analysis for all results.Analysis of variance and independent-samples t-test were used to compare statistical difference of FA values and its SNR;Homogeneity of variance test was adopted to compare statistical difference of variance of FA values.A p-value less than 0.05 was regarded as statistical significance.III.RESULTS The results of statistical analysis of the FA values and its SNR(the mean standard deviation)within 4 ROIs corresponding to 7 different NDGD were listed in Table 1.The results of variance analysis of FA values and its SNR within 4 ROIs between different NDGD were showed in Table 2.Only the SNR of FA values within the ROIs with weaker signals has statistical significance(P0.05).So independent-sample t-test was used to compare the SNR within the ROIs with weaker signals between any 2 NDGDs in the 4 different NDGD(6,12,20,and 30 noncollinear)instead of all the 7 different NDGD(refer to Table 3).The homogeneity test results of the variance of FA values within 4 ROIs between different NDGD were listed in Table 4.The curves of the variance and SNR of FA values within 4 ROIs varying with the NDGD were drawn in terms of Table 1(refer to Figure 3 and 4),respectively.Figure 5 is the curve representing the disperse of the FA values(mean standard deviation)within the ROIs with weaker signals varying with the NDGD.TABLE I.FA VALUES AND ITS SNR(MEAN STANDARD DEVIATION)WITHIN 4 ROIS CORRESPONDING TO ALL 7 DIFFERENT NDGD NDGD FA values SNR of FA values Gcc Scc Gic Plic gcc scc gic plic 6 0.817 0.082 0.781 0.073 0.672 0.065 0.662 0.068 1.775 0.475 1.602 0.405 1.726 0.368 2.032 0.396 9 0.829 0.087 0.754 0.047 0.685 0.048 0.640 0.049 1.821 0.690 1.746 0.357 2.322 0.618 2.833 0.796 12 0.827 0.056 0.783 0.059 0.664 0.036 0.660 0.036 1.907 0.395 1.784 0.286 3.019 0.561 4.207 0.787 15 0.827 0.065 0.788 0.060 0.668 0.030 0.636 0.031 1.782 0.356 1.781 0.278 3.682 0.602 4.774 0.294 20 0.832 0.068 0.774 0.070 0.662 0.027 0.654 0.025 1.943 0.438 1.767 0.269 4.426 0.453 5.215 0.782 25 0.836 0.068 0.774 0.065 0.651 0.026 0.635 0.023 1.935 0.423 1.759 0.267 4.461 0.785 5.369 0.925 30 0.837 0.065 0.772 0.065 0.664 0.026 0.644 0.022 1.933 0.443 1.784 0.314 4.502 0.683 5.394 0.871 TABLE II.VARIANCE ANALYSIS OF FA VALUES AND ITS SNR gcc scc gic plic FA values F 0.071 0.291 0.143 0.216 P 0.999 0.939 0.947 0.916 SNR of the FA values F 0.206 0.344 31.368 28.712 P 0.973 0.910 0.005 0.005 TABLE III.INDEPENDENT-SAMPLE T-TEST FOR SNR OF FA VALUES WITHIN 2 ROIS WITH WEAKER SIGNALS NDGD p gic plic 6 vs 12 0.005 0.01 6vs 20 0.005 0.005 6vs 30 0.005 0.005 12vs20 0.002 0.005 12vs30 0.001 0.005 20vs30 0.582 0.720 TABLE IV.HOMOGENEITY OF VARIANCE TEST FOR FA VALUES gcc scc gic plic p 0.382 0.719 0.002 0.001 IV.DISCUSSION As shown in Table 2,there are no statistical significance in the FA values within all ROIs between any two NDGDs,and the SNR of FA values within the ROIs with stronger signals do not change significantly with the NDGD increasing.Figure 3(a)and(b)illustrates intuitively that there is no clear relationship between the SNRs of the FA values within the ROIs with stronger signals and NDGD,which means that the SNR of the FA values was not obviously improved with NDGD increasing.Table 4 and Figure 4(a)and(b)show that variance of the FA values within ROIs with stronger signals fluctuates randomly,i.e.it has nothing to do with NDGD changing.It is thus clear that increasing NDGD has no significant for the ROIs with stronger signals,to which NDGD=6 might be a good choice.This is consistent with the conclusion suggesting that NDGD=6 is sufficient for estimation of FA values 5.However,as shown in Figure 5,the variance of FA values within ROIs with weaker signals gradually diminish with NDGD increasing.This indicates that as the NDGD increasing,fluctuation of FA values within these ROIs decreases,the precision is improved.Table 4 also demonstrates that the variance of FA values within the two ROIs has statistical significance among 7 different NDGD(P0.05).Variance of FA value within the ROIs versus NDGD is obviously illustrated in Figure 4(c)and(d),from which,it is known that variance of FA values within the ROIs diminishes significantly with NDGD increasing from 6 to 20,and that diminishes slowly in the range from 20 to 30.As shown in Table 2,the SNR of FA values within the two ROIs also has statistical significance(P0.05).From the results of the independentsample t-test between any two NDGDs(refer to Table 3),it can be seen that the SNR of FA values is improved remarkably(P0.05).Figure 3(c)and(d)shows more obviously that the SNR of the FA values within the ROIs gets a linearly improvement when NDGD increases from 6 to 20,but from 20 to 30,the SNR becomes to a nearly stable level.The result demonstrates that within the ROIs whose SNR is relatively low,as Gic and Plic selected in the paper,NDGD has an obvious influence on fluctuation range and SNR of the FA values.But the fluctuation of the FA values becomes to stable and SNR no more improves when the NDGD is more than 20,which means that NDGD has little contribution to SNR of FA values when the NDGD is more than 20,under this condition,there is no substantial significance to increase the NDGD.So it may be better to choose the NDGD=20 for detecting the FA values from ROIs with weaker signals to reduce scanning time and eliminate movement-induced artifacts.This is consistent with the conclusion that 20-diffusion gradients may be probably sufficient for in vivo human study of diffusion anisotropy 9.It is also agreed with the conclusion by Papadakis NG et al 12 that the minimum NDGD required for robust anisotropy estimation is between 18 and 21.Therefore,in clinical applications of DTI,an optimum NDGD for DTI data acquisition should be selected according to the ROIs in human brain to be inspected.(a)(b)(c)(d)Figure 3.SNR of the FA values within 4 ROIs versus NDGD (a)(b)(c)(d)Figure 4.Variance of FA values within 4 ROIs versus NDGD Figure 5.The graphics of fluctuation of FA values within 2 ROIs with weaker signals V.CONCLUSION It is no necessary to increase NDGD for ROIs with stronger signals,and NDGD=6 may be a good choice.In the ROIs with weaker signals,however,dispersion degree of the FA values diminishes and the SNR is higher and higher with the NDGD increasing.Variance of the FA values becomes to stable when NDGD=20 and the SNR of the FA values almost stop increasing at the same time.So it is preferable to choose NDGD=20 for detecting DTI signals from the ROIs with weaker signals to reduce scanning time to eliminate movement-induced artifacts.ACKNOWLEDGMENT We are grateful to Johns Hopkins Medical Institute Laboratory of Brain Anatomical MRI for permitting us download and use the DTI data.We would like to thank Dr.Hangyi Jiang who works in Johns Hopkins University for supplying the software(DTI Studio)for our study.Finally,we would like to thank the reviewers for their valuable remarks.REFERENCES 1 Charalambos Bougias,Evanthia E.Tripoliti.Theory of diffusion tensor imaging and fiber tractography analysis.European Journal of Radiography(2009)1,37-41 2 Dongrong Xu,Jiali Cui,Ravi Bansal,et al.The ellipsoidal area ratio:an alternative anisotropy index for diffusion tensor imaging.Magnetic Resonance Imaging 27(2009)311323 3 P.J.Basser,J.Mattiello,D.LeBihan.(1994)Estimation of the effective selfdiffusion tensor from theNMRspin echo.JMagn Reson B,103,247254.4 Andrew L.Alexander,Jee Eun Lee,Mariana Lazar,and Aaron S.Field.Diffusion Tensor Imaging of the Brain.Neurotherapeutics,Vol.4,No.3,2007.316-329 5 H.Ni,V.Kavcic.T.Zhu,et al.Effects of Number of Diffusion Gradient Directions on Derived Diffusion Tensor Imaging Indices in Human Brain.AJNR Am J Neuroradiol,2006.27:1776-8.6 Na Zhang,Zhen-Sheng Deng,Fang Wang,Xiao-Yi Wang.The effect of different number of diffusion gradients on SNR of diffusion tensor-derived measurement maps.J.Biomedical Science and Engineering,2009.2:96-101.7 N.G.Papadakis,D.Xing,G.C.Houston,et al.A study of rotational invariant and symmetric indices of diffusion anisotropy.Magn Reson Imaging,1999.17:88192.8 S.Skare,M.Hedehus,M.E.Moseley,et al.Condition number as a measure of noise performance of diffusion tensor data acquisition schemes with MRI.J Magn Reson,2000.147:34052.9 D.K.Jones.The effect of gradient sampling schemes on measures derived from diffusion tensor MRI:a Monte Carlo study.Magn Reson Med,2004.51:80715.10 Setsu Wakana,Hangyi Jiang,and Lidia M.Nagae-Poetscher et al.Fiber Tractbased Atlas of Human White Matter Anatomy.Radiology,January 2004,p77-87 11 H.Jiang,P.C.M.van Zijl,et al.DtiStudio:Resource program for diffusion tensor computation and fiber bundle puter methods and programs in biomedicine,2006.81:106116.12 Papadakis NG,Murrills CD,Hall LD,et al.Minimal gradient encoding for robust estimation of diffusion anisotropy.Magn Reson Imaging 2000;18:67179.。